More axiomatics for the Hirsch index

The Hirsch index is a number that synthesizes a researcher’s output. It is defined as the maximum number h such that the researcher has h papers with at least h citations each. Woeginger (Math Soc Sci 56: 224–232, 2008a; J Informetr 2: 298–303, 2008b) suggests two axiomatic characterizations of the Hirsch index using monotonicity as one of the axioms. This note suggests three characterizations without adopting the monotonicity axiom.     

Paretian publication patterns imply Paretian Hirsch index

The paper pursues the rigorous mathematical study of the Hirsch index and shows that it has power law upper tail distribution and determines the exponent provided that the underlying publication and citation distributions have fat tails as well. The result is demonstrated on the distribution of the Hirsch index of journals. The paper is concluded with some further remarks on the Hirsch index.     

Hirsch index or Hirsch rate? Some thoughts arising from Liang’s data

Hirsch’s h-index gives a single number that in some sense summarizes an author’s research output and its impact. Since an individual author’s h-index will be time-dependent, we propose instead the h-rate which, according to theory, is (almost) constant. We re-analyse a previously published data set (Liang, 2006) which, although not of the precise form to properly test our model, reveals that in many cases we do not have a constant h-rate. On the other hand this then suggests ways in which deeper scientometric investigations could be carried out. This work should be viewed as complementary to that of Liang (2006).     

The Hirsch index in manufacturing and Quality engineering

The Hirsch index (h) is a recent bibliometric indicator for assessing the research output of scientists. Its most remarkable characteristics are immediate intuitive meaning, effective synthesis and easy calculation. With few modifications, the use of this indicator can be profitably extended to other fields beyond bibliometrics. The main novelty of the paper is to suggest some potential applications in manufacturing and Quality engineering, focussing the attention on the h capacity to aggregate and synthesize the most commonly used metrics in these areas. Copyright © 2009 John Wiley & Sons, Ltd.     

Citations versus limitations of citations: beyond Hirsch index

It appears popular, particularly among science administrators, to use citations and various citation measures for ranking scientists, as if such exercises would reflect the scientific potential of the persons considered. In recent time the Hirsch index h in particular has obtained visibility in this respect in view of its simplicity. We consider a possible extension of the concept of selective citations, which in fact is innate to the h index, and propose a simple generalization, indices H and Q, which to a degree supplement the information accompanying the evaluation of h. The H index keeps record of the “history” of citations and the quotient Q = H/h is a measure for the quality of a scientist based on the history of his/her citations.     

An extension of the Hirsch index: Indexing scientific topics and compounds

Summary An interesting twist of the Hirsch index is given, in terms of an index for topics and compounds. By comparing both the hb index and m for a number of compounds and topics, it can be used to differentiate between a new so-called hot topic with older topics. This quick method is shown to help new comers to identify how much interest and work has already been achieved in their chosen area of research.     

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

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)^1/2 ≈ h, 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.     

Further aspects of the British index of secondary car safety

This paper develops earlier research into statistical methods for comparing the secondary safety of car models. Two papers (Broughton 1996a,b, Accident Analysis and Prevention, Vol. 28, pp. 89–99, and pp. 101–109, respectively) had concluded that the most satisfactory index of secondary safety is the one first used in publications of the U.K. Department of Transport, referred to as the British or DoT index. This paper shows that the distribution of the risk of injury when two cars collide depends principally on the difference in mass; as this rises, the driver of the lighter car is more likely to be injured and the driver of the heavier car is less likely to be injured, while the likelihood of both being injured reduces slightly. It also shows that the level of protection in fatal and serious accidents varies between models to a significantly greater extent than the level in all injury accidents. Car models of similar mass can provide significantly different levels of protection to their occupants, so there would be fewer casualties if all models were to provide the same level of protection as the most successful current designs. It is estimated that if the safety of all models were improved to the level achieved or exceeded by the safest twentieth of models then the number of drivers injured in two-car accidents would fall by 12% and the number killed or seriously injured by 22%.     

Further trials of a strain hardening index of fatigue damage

Previous cyclic-strain, smooth-specimen fatigue tests of α–β titanium alloys displayed an anomolous endurance enhancement for some of the alloy conditions. This could be explained by associating resistance to fatigue damage directly with the stress-normalized plastic strain hardening rate at the point of maximum cyclic tensile stress. Since this rate also controls the extent of stress-relaxation-induced tensile creep strain in each cycle, it was thought that fatigue damage might be associated with it. To test this hypothesis, data with varied load hold time, and over a full range of cyclic life, is reported here for some of the previously reported alloys of Ti-6A1-4V, as well as for an A36 steel plate. Notch fatigue tests of the A36, combined with those of Yoder et al. for the titanium alloys, are compared to the smooth specimen data. Results tend to support the damage-inhibiting role of the plastic strain hardening rate, but not of the creep strain portion of each cycle. Notch fatigue data agrees with smooth specimen trends if Neuber's rule is used to characterize the stress concentration factor, particularly with the A36 steel. As with Yoder's notch fatigue results, smooth specimen LCF life, though quite different in the range less than 10³ cycles, tends to converge near the endurance limit, thus mitigating adverse effects of alloy conditions which favor resistance to fatigue crack propagation in α-β titanium alloys.     

A multidimensional extension to Hirsch’s h-index

The h-index is becoming a reference tool for career assessment and it is starting to be considered by some agencies and institutions in promotion, allocation, and funding decisions. In areas where h indices tend to be low, individuals with different research accomplishments may end up with the same h. This paper proposes a multidimensional extension of the h index in which the conventional h is only the first component. Additional components of the multidimensional index are obtained by computing the h-index for the subset of papers not considered in the immediately preceding component. Computation of the multidimensional index for 204 faculty members in Departments of Methodology of the Behavioral Sciences in Spain shows that individuals with the same h can indeed be distinguished by their values in the remaining components, and that the strength of the correlation of the second and third components of the multidimensional index with alternative bibliometric indicators is similar to that of the first component (i.e., the original h).     

Generalized Hirsch h-index for disclosing latent facts in citation networks

What is the value of a scientist and its impact upon the scientific thinking? How can we measure the prestige of a journal or a conference? The evaluation of the scientific work of a scientist and the estimation of the quality of a journal or conference has long attracted significant interest, due to the benefits by obtaining an unbiased and fair criterion. Although it appears to be simple, defining a quality metric is not an easy task. To overcome the disadvantages of the present metrics used for ranking scientists and journals, J. E. Hirsch proposed a pioneering metric, the now famous h-index. In this article we demonstrate several inefficiencies of this index and develop a pair of generalizations and effective variants of it to deal with scientist ranking and publication forum ranking. The new citation indices are able to disclose trendsetters in scientific research, as well as researchers that constantly shape their field with their influential work, no matter how old they are. We exhibit the effectiveness and the benefits of the new indices to unfold the full potential of the h-index, with extensive experimental results obtained from the DBLP, a widely known on-line digital library.     

Parametric characterizations in superparamagnetic latex

The effect of synthesis parameters on the production of superparamagnetic latex, which are magnetite nanoparticles covered with a poly(methyl methacrylate) layer, were studied. The synthesis method was based on the developed route of emulsifier-free emulsion polymerization. Under this study, effects of the monomer and initiator concentrations, the amount of magnetic sol, the stirring rate and the adding rate of the magnetic sol on the properties of synthesized latexes were investigated. The characterizations were performed by a high resolution transmission electron microscopy, a dynamic light scattering, a vibrating sample magnetometer and a gel permeation chromatography. The results showed that the monomer concentration was found to be the most effective parameter on latex stability. As the initiator amount and the stirring rate increased, saturation magnetization and average molecular weight decreased due to the reactions occurring between surfaces of magnetite nanoparticles and initiator fragments. On increasing amount of magnetic sol, the saturation magnetization and polymer molecular weight increased but the size of nanospheres was unchanged because of the ions in magnetic sol. It was seen that the desired size and magnetic properties of the latex could be obtained since the parameters were found to have substantial impact on their properties.     

Surface characterizations of ultrafine Ni particles

Ultrafine Ni particles have been obtained by evaporating pure Ni in methane gas atmosphere of 100 Torr, and in a mixture of H₂ and Ar of 760 Torr, respectively. The distinct characterization of the layers on two kinds of Ni particle surfaces were investigated by X-ray photoelectron spectroscopy (XPS) and oxygen determination. The morphology and mean particle size were determined by transmission electron spectroscopy (TEM) and subsequent image analysis. The structure of ultrafine Ni particles were identified by X-ray diffraction (XRD). The effect of oxide and carbon layers on magnetization of the particles were studied by vibrating sample magnetometer (VSM). It was observed that a carbon-rich and an oxide of Ni₂O₃ layers were formed on the surface of Ni particles obtained in methane gas, and in a mixture of H₂ and A_r gas atmosphere, respectively. It was shown that the methane gas makes resistance to oxidization during evaporating Ni in this gas atmosphere and no nickel carbides or Ni-C solid solutionformed.     

Eliminating nuisance parameters: two characterizations

Given a statistical modelP = {P_θ : θ ∈ x} and a surjective functiong: ϑ→Λ the problem of transformingP into a new modelQ= {_λ : λ ∈ Λ} indexed by Λ is investigated. Two characterizations are given for those modelsQ of the form Q_λ = ∫ P_θ π_λ(dθ), where π_λ is some probability such that π_λ(g=λ)=1. The first is related to a geometric property ofQ, while the second rests on the inferential implications of adoptingQ. Also, in the first π_λ is allowed to be finitely additive, while in the second π_λ is σ-additive. Finally, integrated likelihoods are revisited in light of the second characterization.     

Submicron bubble garnets and their characterizations

New Submicron (0.5-1.0 mum diam) bubble garnets have been developed. In order to reduce saturation induction4piMsas low as possible, suitable choice of amounts of nonmagnetic ions substituting for ferric ions in both tetrahedral and octahedral sites were studied in (YSm)3(FeAl)5O12, (YSmLu)3- (FeGaSc)5O12, (YSmLu)3(FeAlSc)5O12and (LaLuSm)3- (FeGa)5O12garnet systems. For example, in (YSmLu)3- (FeAlSc)5O12a film with the following properties was grown; strip widthw = 0.7mum, film thicknessh= 0.7mum, quality factorq=2.8, Curie temperatureTc= 140degC and4piMs=770G. The temperature properties of those films could be improved drastically by doping with a small amount of Gd ion. Wall mobilities μw of those films are in the region from 200 to 500cm/s/Oe. Preceding these material studies, several film characterization methods have been investigated. Film thickness was measured by Fluorescent X-ray method, strip width by using a highly sensitivity TV camera, and bubble collapse field by FMR resonance technique respectively.     

Some characterizations of the optimal solutions of a vector optimization problem

Summary In this paper several kinds of optima of a vector optimization problem are investigated; these are minimal, weakly minimal, strongly minimal and properly minimal solutions. For these optima various optimality conditions resulting from a scalarization approach are presented. Furthermore some numerical aspects are discussed.

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Zusammenfassung In dieser Arbeit werden einige Arten von Optima eines Vektoroptimierungsproblems untersucht. Es handelt sich dabei um minimale, schwach minimale, stark minimale und eigentlich minimale Lösungen. Für diese Optimalitätsbegriffe werden verschiedene Optimalitätsbedingungen vorgestellt, die sich durch Skalarisierung ergeben. Außerdem wird auf einige numerische Aspekte eingegangen.

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Parts of this paper were written when the author was a visitor at the Department of Mathematics of North Carolina State University, Raleigh, North Carolina 27695-8205, USA     

A Hirsch measure for the quality of research supervision,and an illustration with trade economists

There is a growing literature measuring research excellence in economics. The h-index is noteworthy in combining quantity and research quality in a single measure of researcher excellence, and its ability to be extended to measure the quantity and quality of the researchers in a department. We extend the use of the first successive h-index further to measure the quality of graduate education, specifically excellence in research supervision, based on publication and citation data for individual researchers ascribed to their graduate supervisors.     

Investigation of fracture characterizations of functionally graded materials

In this paper, the mode I crack problem of functionally gradient materials (FGMs) with the gradient direction parallel to the crack is discussed, and the differences of stress distribution between the gradient materials and the homogeneous materials are analyzed. It is shown that a mode I crack problem of FGMs with the gradient direction parallel to the crack direction can become a mixed‐mode crack problem. In FGMs, the crack initiation angles are determined by the fracture toughness gradient, elastic modulus and crack mode. If the gradient coefficients are small, the crack initiation angles in FGMs are the same as those in homogeneous materials. If the elastic modulus gradient is large, the principal stress terms without the gradient coefficients can be ignored in obtaining the crack initiation angle. In this study, all the above results are generalized to the mixed‐mode crack problems with arbitrary angle between the gradient direction and the crack direction.     

Pulsed laser deposition and optical characterizations of the magnetic samarium orthoferrite

Pulsed Laser Deposition of magnetically ordered polycrystalline SmFeO₃ films has been optimized onto SiO₂ glass substrates as function of substrate temperature, oxygen pressure and pulsed laser fluency. Using a KrF excimer laser, crystallization temperature is found to be about 1048 K for a weak fluency of only 1.7 J cm^− 2. We show that this growth temperature can be reduced using higher fluency and that it is possible to obtain a film texturation along the c axis by reducing the oxygen pressure at given temperature and fluency. In a second part, we focus on the SmFeO₃ optical constants determined by in situ ellipsometry using a stacking model and the Cauchy dispersion relation for SmFeO₃ layer. We show a good correlation between the transmission and reflection calculated from these data and measured by ex situ spectrophotometry in the visible range.