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Abstract

The Hsinchu Science Park in Taiwan has been synonymous with dynamic and flourishing high-tech industries and companies since the 1980s. Using patent citation data, this empirical study shows that Taiwan's Hsinchu Science Park is a healthy and knowledge-based cluster surrounded by the semiconductor sector, in which external knowledge is continuously playing an important role, while internalized capability is building up quickly; new and extended industrial clusters are being established by the growth of new ventures; and the linkages of capital, manpower, and technology flows are conducted respectively by the large business groups, the NTHU and NCTU, and the ITRI in the region. Subsequent sectors, repeating the successful model created by and catalyzed from the semiconductor sector are flourishing; the thin-film transistor-liquid crystal display (TFT-LCD) and integrated circuit (IC) design sectors have been growing rapidly since the beginning of the 2000s, and the solar photovoltaic and LED (Light-Emitting Diode) sectors emerged quickly in mid-2005. The continuous evolving and growing industries along with the significant increase of value added in the Hsinchu Science Park have demonstrated it is acting as a healthy and vivid innovation region. The policy implications derived from this study can thus shed light, for the Southeast Asian, Latin American or other latecomers, on the strategies for formulating regional research and innovation policies in the process of developing a knowledge-based economy.

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Abstract

The aim of this paper is to identify the research paradigms on digital libraries in China while compared with that of international digital libraries research via scientometric analysis. Co-word network constructed by keywords in documents and their co-occurrence relationships is a kind of mapping knowledge domains, which represents the cognitive and intellectual structure of science. A total of 6068 and 1250 papers published between 1994 and 2010 were, respectively retrieved from the China National Knowledge Infrastructure (CNKI) and ScienceDirect databases with a topic search of digital libraries or digital library in abstracts of papers. This paper uses methods of co-word analysis, social network analysis and mapping knowledge domains as theory basis, with assistance of softwares of UCINET and Netdraw, to construct the co-word network of digital libraries/library research in China, present the study status quo and evolution on digital libraries/library in China and analyze the research paradigm structure of digital libraries/library in China.

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Authors: Jiagui Luo and Pingzhi Yuan

Abstract

We obtain all solutions of the equation with c∊{±1,±2,±4}.

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Abstract

The objective of this paper is to offer sufficient conditions for the oscillation of all solutions and other asymptotic properties of the third-order nonlinear functional differential equation

ea
with mixed arguments, where both cases ∫ a −1/γ(s) ds=∞ and ∫ a −1/γ(s) ds<∞ are dealt with. We deduce properties of the studied equations via new comparison theorems. Our results essentially improve and complement earlier ones. We also repair one interesting result of Grace et al.

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Authors: Giovanni Abramo, Ciriaco Andrea D’Angelo and Flavia Di Costa

Abstract

This work analyses the links between individual research performance and academic rank. A typical bibliometric methodology is used to study the performance of all Italian university researchers active in the hard sciences, for the period 2004–2008. The objective is to characterize the performance of the ranks of full (FPs), associate and assistant professors (APs), along various dimensions, in order to verify the existence of performance differences among the ranks in general and for single disciplines.

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Authors: Santanu Bhunia, Pratulananda Das and Sudip Kumar Pal

Abstract

We first introduce a new notion called statistical convergence of order α and primarily show that it gives rise to a decreasing chain of closed linear subspaces of the space of all bounded real sequences with sup norm which never coincides with the class of convergent sequences and in fact their intersection properly contains the class of convergent sequences. We then show that the same method can be applied for double sequences also and introduce the notion of statistical convergence of order (α,β).

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Abstract

We prove that the conjugate convolution operators can be used to calculate jumps for functions. Our results generalize the theorems established by He and Shi. Furthermore, by using Lukács and Móricz's idea, we solve an open question posed by Shi and Hu.

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Abstract

In reaction to a previous critique (Opthof and Leydesdorff, J Informetr 4(3):423–430, ), the Center for Science and Technology Studies (CWTS) in Leiden proposed to change their old “crown” indicator in citation analysis into a new one. Waltman (Scientometrics 87:467–481, ) argue that this change does not affect rankings at various aggregated levels. However, CWTS data is not publicly available for testing and criticism. Therefore, we comment by using previously published data of Van Raan (Scientometrics 67(3):491–502, to address the pivotal issue of how the results of citation analysis correlate with the results of peer review. A quality parameter based on peer review was neither significantly correlated with the two parameters developed by the CWTS in the past citations per paper/mean journal citation score (CPP/JCSm) or CPP/FCSm (citations per paper/mean field citation score) nor with the more recently proposed h-index (Hirsch, Proc Natl Acad Sci USA 102(46):16569–16572, ). Given the high correlations between the old and new “crown” indicators, one can expect that the lack of correlation with the peer-review based quality indicator applies equally to the newly developed ones.

Open access

Abstract

We study the spectral multiplicity for the direct sum AB of operators A and B on the Banach spaces X and Y. Under some domination conditions ‖P(B)‖≦CP(A)‖, in particular, ‖B n‖≦CA n‖, n≧0, we prove the addition formulas μ(AB)=μ(A)+μ(B) for spectral multiplicities. We give valuable new applications of the main result of the author’s paper [12]. We also use the so-called Borel transformation and generalized Duhamel product in calculating the spectral multiplicity of a direct sum of the form TA, where T is a weighted shift operator on the Wiener algebra .

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Abstract

We consider fourth order quasilinear ordinary differential equations. Firstly, we classify positive solutions into four types according to their asymptotic properties. Then we derive existence theorems of positive solutions belonging to each type. Using these results, we can obtain an oscillation criterion, which is our main objective. Moreover, applying such criteria for ordinary differential equations to binary elliptic systems, we establish nonexistence theorems for positive solutions.

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Authors: Afshin Amini, Babak Amini, Ehsan Momtahan and Mohammad Hassan Shirdareh Haghighi

Abstract

We associate a graph Γ+(R) to a ring R whose vertices are nonzero proper right ideals of R and two vertices I and J are adjacent if I+J=R. Then we try to translate properties of this graph into algebraic properties of R and vice versa. For example, we characterize rings R for which Γ+(R) respectively is connected, complete, planar, complemented or a forest. Also we find the dominating number of Γ+(R).

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Abstract

A nonnegative linear relation S in a Hilbert space ℌ is assumed to intertwine in a certain sense two bounded everywhere defined operators B and C. A related quotient of the range of S is then provided with a natural inner product and the operators B and C induce two operators on the completion space. This construction is used to show the existence of self-adjoint and nonnegative extensions of the linear relations B S and C S, respectively.

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Abstract

Given a finite family of linear forms with integer coefficients, and a compact abelian group G, an -free set in G is a measurable set which does not contain solutions to any equation L(x)=0 for L in . We denote by the supremum of μ(A) over -free sets AG, where μ is the normalized Haar measure on G. Our main result is that, for any such collection of forms in at least three variables, the sequence converges to as p→∞ over primes. This answers an analogue for ℤp of a question that Ruzsa raised about sets of integers.

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Authors: F. Camargo, A. Caminha, H. de Lima and M. Velásquez

Abstract

We study several aspects of the geometry of conformally stationary Lorentz manifolds, and particularly of GRW spaces, due to the presence of a closed conformal vector field. More precisely, we begin by extending a result of J. Simons on the minimality of cones in Euclidean space to these spaces, and apply it to the construction of complete, noncompact minimal Lorentz submanifolds of both de Sitter and anti-de Sitter spaces. Then we state and prove very general Bernstein-type theorems for spacelike hypersurfaces in conformally stationary Lorentz manifolds, one of which not assuming the hypersurface to be of constant mean curvature. Finally, we study the strong r-stability of spacelike hypersurfaces of constant r-th mean curvature in a conformally stationary Lorentz manifold of constant sectional curvature, extending previous results in the current literature.

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Abstract

A. Dubickas and C. Smyth introduced the metric Mahler measure

ea
where M(α) denotes the usual (logarithmic) Mahler measure of . This definition extends in a natural way to the t-metric Mahler measure by replacing the sum with the usual L t norm of the vector (M(α 1),…,M(α N)) for any t≧1. For α∊ℚ, we prove that the infimum in M t(α) may be attained using only rational points, establishing an earlier conjecture of the second author. We show that the natural analogue of this result fails for general by giving an infinite family of quadratic counterexamples. As part of this construction, we provide an explicit formula to compute M t(D 1/k) for a squarefree D∊ℕ.

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Authors: Villő Csiszár, Péter Hussami, János Komlós, Tamás F. Móri, Lídia Rejtő and Gábor Tusnády

Abstract

There is a uniquely defined random graph model with independent adjacencies in which the degree sequence is a sufficient statistic. The model was recently discovered independently by several authors. Here we join to the statistical investigation of the model, proving that if the degree sequence is in the interior of the polytope defined by the Erdős–Gallai conditions, then a unique maximum likelihood estimate exists.

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Abstract

This paper suggests a method for Subject–Action–Object (SAO) network analysis of patents for technology trends identification by using the concept of function. The proposed method solves the shortcoming of the keyword-based approach to identification of technology trends, i.e., that it cannot represent how technologies are used or for what purpose. The concept of function provides information on how a technology is used and how it interacts with other technologies; the keyword-based approach does not provide such information. The proposed method uses an SAO model and represents “key concept” instead of “key word”. We present a procedure that formulates an SAO network by using SAO models extracted from patent documents, and a method that applies actor network theory to analyze technology implications of the SAO network. To demonstrate the effectiveness of the SAO network this paper presents a case study of patents related to Polymer Electrolyte Membrane technology in Proton Exchange Membrane Fuel Cells.

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The algorithms of Shimoyama and Yokoyama for primary decomposition of ideals are generalized to submodules of a free module over the polynomial ring in several variables with coefficients in a field. The algorithms are implemented in Singular.

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In the applications it may occur that our initial pseudorandom binary sequence is not long enough, thus we have to take the concatenation of it with another pseudorandom binary sequences. Here we will consider concatenation of Legendre symbol sequences so that the resulting longer sequence has strong pseudorandom properties.

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In this paper we study I-approximation properties of certain class of linear positive operators. The two main tools used in this paper are I-convergence and Ditzian-Totik modulus of smoothness. Furthermore, we define q-Lupaş-Durrmeyer operators and give local and global approximation results for such operators.

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Authors: Roma kačinskaitė and Antanas Laurinčikas

In this paper, the joint approximation of a given collection of analytic functions by a collection of shifts of zeta-functions with periodic coefficients is obtained. This is applied to prove the functional independence for these zeta-functions.

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The midpoint set M(S) of a set S of points is the set of all midpoints of pairs of points in S. We study the largest cardinality of a midpoint set M(S) in a finite-dimensional normed space, such that M(S) is contained in the unit sphere, and S is outside the closed unit ball. We show in three dimensions that this maximum (if it exists) is determined by the facial structure of the unit ball. In higher dimensions no such relationship exists. We also determine the maximum for euclidean and sup norm spaces.

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An abelian p-group G has a nice basis if it is the ascending union of a sequence of nice subgroups, each of which is a direct sum of cyclic groups. It is shown that if G is any group, then GD has a nice basis, where D is the divisible hull of p ω G. This leads to a consideration of the nice basis rank of G, i.e., the smallest rank of a divisible group D such that GD has a nice basis. This concept is used to show that there exist a reduced group G and a non-reduced group H, both without a nice basis, such that GH has a nice basis

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Authors: Ludo Waltman, Nees Jan van Eck, Thed N. van Leeuwen, Martijn S. Visser and Anthony F. J. van Raan

Abstract

Opthof and Leydesdorff (Scientometrics, ) reanalyze data reported by Van Raan (Scientometrics 67(3):491–502, ) and conclude that there is no significant correlation between on the one hand average citation scores measured using the CPP/FCSm indicator and on the other hand the quality judgment of peers. We point out that Opthof and Leydesdorff draw their conclusions based on a very limited amount of data. We also criticize the statistical methodology used by Opthof and Leydesdorff. Using a larger amount of data and a more appropriate statistical methodology, we do find a significant correlation between the CPP/FCSm indicator and peer judgment.

Open access

The limit q-Bernstein operator B q = B ∞,q: C[0, 1] → C[0, 1] emerges naturally as a q-version of the Szász-Mirakyan operator related to the q-deformed Poisson distribution. The latter is used in the q-boson theory to describe the energy distribution in a q-analogue of the coherent state.The limit q-Bernstein operator has been widely studied lately. It has been shown that B q is a positive shape-preserving linear operator on C[0, 1] with ‖B q‖ = 1. Its approximation properties, probabilistic interpretation, behavior of iterates, and the impact on the smoothness have been examined.In this paper, it is shown that the possibility of an analytic continuation of B q f into {z: |z| < R}, R > 1, implies the smoothness of f at 1, which is stronger when R is greater. If B q f can be extended to an entire function, then f is infinitely differentiable at 1, and a sufficiently slow growth of B q f implies analyticity of f in {z: |z − 1| < δ}, where δ is greater when the growth is slower. Finally, there is a bound for the growth of B q f which implies f to be an entire function.

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In this paper, we prove that a space X is a weak-open compact image of a locally separable metric space if and only if X has a uniform cosmic-weak-base if and only if X is a weak-open compact image of a metric space and a locally cosmic space, and give some internal characterizations of weak-open s-images of locally separable metric spaces.

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Abstract

This paper by using data envelopment analysis (DEA) and statistical inference evaluates the citation performance of 229 economic journals. The paper categorizes the journals into four main categories (A–D) based on their efficiency levels. The results are then compared to the 27 “core economic journals” as introduced by Diamond (Curr Contents 21(1):4–11, ). The results reveal that after more than 20 years Diamonds’ list of “core economic journals” is still valid. Finally, for the first time the paper uses data from four well-known databases (SSCI, Scopus, RePEc, Econlit) and two quality ranking reports (Kiel Institute internals ranking and ABS quality ranking report) in a DEA setting and in order to derive the ranking of 229 economic journals. The ten economic journals with the highest citation performance are Journal of Political Economy, Econometrica, Quarterly Journal of Economics, Journal of Financial Economics, Journal of Economic Literature, American Economic Review, Review of Economic Studies, Journal of Econometrics, Journal of Finance, Brookings Papers on Economic Activity.

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Abstract

With the modern technology fast developing, most of entities can be observed by different perspectives. These multiple view information allows us to find a better pattern as long as we integrate them in an appropriate way. So clustering by integrating multi-view representations that describe the same class of entities has become a crucial issue for knowledge discovering. We integrate multi-view data by a tensor model and present a hybrid clustering method based on Tucker-2 model, which can be regarded as an extension of spectral clustering. We apply our hybrid clustering method to scientific publication analysis by integrating citation-link and lexical content. Clustering experiments are conducted on a large-scale journal set retrieved from the Web of Science (WoS) database. Several relevant hybrid clustering methods are cross compared with our method. The analysis of clustering results demonstrate the effectiveness of the proposed algorithm. Furthermore, we provide a cognitive analysis of the clustering results as well as the visualization as a mapping of the journal set.

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Authors: Daniel Torres-Salinas, Jose G. Moreno-Torres, Emilio Delgado-López-Cózar and Francisco Herrera

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The problem of comparing academic institutions in terms of their research production is nowadays a priority issue. This paper proposes a relative bidimensional index that takes into account both the net production and the quality of it, as an attempt to provide a comprehensive and objective way to compare the research output of different institutions in a specific field, using journal contributions and citations. The proposed index is then applied, as a case study, to rank the top Spanish universities in the fields of Chemistry and Computer Science in the period ranging from 2000 until 2009. A comparison with the top 50 universities in the ARWU rankings is also made, showing the proposed ranking is better suited to distinguish among non-elite universities.

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Abstract  

Using classical analytic techniques, a double inequality for differences of power means and geometric means in two variables is generalized and sharpened. A new inequality for differences of power means involving four parameters is established.

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We prove the equivalence of some three-weighted criteria for the boundedness of Hardy type operators on the cone of decreasing functions. These criteria are then applied to realize the direct comparisons of the results obtained in different forms in the papers of several authors (M. Goldman, G. Bennett and K.-G. Grosse-Erdmann, M. Carro, A. Gogatishvili, J. Martin, and L. Pick).

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Реэюме  

В работе построены раэложения тождественного оператора в пространстве L p(I d) в кратные ряды иэ ортопроекционных операторов на вэаимно ортогональные подпространства кусочно-полиномиальных функции, частным случаем которых является ряд Хаара. Юстановлены оценки норм в L p(I d) соответствуюших проекции. С их помошью получены оценки колмогоровского n-поперечника в пространстве L 2(I d) для единичных щаров пространств Никольского и QBесова функции, удовлетворяюших смещанным условиям Гёльдера, даюшие порядок тои величины.

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Authors: Hui-Zhen Fu, Kun-Yang Chuang, Ming-Huang Wang and Yuh-Shan Ho

Abstract

To provide an overview of the characteristics of research in China, a bibliometric evaluation of highly cited papers with high-level representation was conducted during the period from 1999 to 2009 based on the Essential Science Indicators (ESI) database. A comprehensive assessment covered overall performance, journals, subject categories, internationally collaborative countries, national inter-institutionally collaborative institutions, and most-cited papers in 22 scientific fields. China saw a strong growth in scientific publications in the last decade, to some extent due to increasing research and development expenditure. China has been more active in ESI fields of chemistry and physics, but more excellent in materials science, engineering and mathematics. Most publications were concerned with the common Science Citation Index subject categories of multidisciplinary chemistry, multidisciplinary materials and science, and physical chemistry. About one half China's ESC papers were internationally collaborative and the eight major industrialized countries (the USA, Germany, the UK, Japan, France, Canada, Russia, and Italy) played a prominent role in scientific collaboration with China, especially the USA. The Chinese Academy of Sciences took the leading position of institutions with many branches. The “985 Project” stimulated the most productive institutions for academic research with a huge funding injection and the universities in Hong Kong showed good scientific performance. The citation impact of internationally collaborative papers differed among fields and international collaborations made positive contributions to academic research in China.

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Abstract

In academia, the term “inbreeding” refers to a situation wherein PhDs are employed in the very same institution that trained them during their doctoral studies. Academic inbreeding has a negative perception on the account that it damages both scientific effectiveness and productivity. In this article, the effect of inbreeding on scientific effectiveness is investigated through a case study. This problem is addressed by utilizing Hirsch index as a reliable metric of an academic's scientific productivity. Utilizing the dataset, constructed with academic performance indicators of individuals from the Mechanical and Aeronautical Engineering Departments, of the Turkish Technical Universities, we demonstrate that academic inbreeding has a negative impact on apparent scientific effectiveness through a negative binomial model. This model appears to be the most suitable one for the dataset which is a type of count data. We report chi-square statistics and likelihood ratio test for the parameter alpha. According to the chi-square statistics the model is significant as a whole. The incidence rate ratio for the variable “inbreeding” is estimated to be 0.11 and this ratio tells that, holding all the other factors constant, for the inbred faculty, the h-index is about 89% lower when compared to the non-inbred faculty. Furthermore, there exists negative and statistically significant correlation with an individual's productivity and the percentage of inbred faculty members at the very same department. Excessive practice of inbreeding adversely affects the overall productivity. Decision makers are urged to limit this practice to a minimum in order to foster a vibrant research environment. Furthermore, it is also found that scientific productivity of an individual decreases towards the end of his scientific career.

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Abstract

The single publication H-index, introduced by A. Schubert in 2009 can be applied on all articles in the Hirsch-core of a researcher. In this way one can define the “indirect H-index” of a researcher.

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This paper provides an overview of the progression of technology structure based on patent co-citation networks. Methods of patent bibliometrics, social network analysis and information visualization are employed to analyze patents of Fortune 500 companies indexed in Derwent Innovations Index, the largest patent database in the world. Based on the co-citation networks, several main technology groups are identified, including Chemicals, Petroleum Refining, Motor Vehicles, Pharmaceuticals, Electronics, etc. Relationships among the leading companies and technology groups are also revealed.

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We obtain necessary conditions for a doubly triangular matrix A to have the property that a double series ΣΣ λmn b mn is summable |A|k whenever the series ΣΣb mn is bounded |A|k.

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We prove that the “quadratic irrational rotation” exhibits a central limit theorem. More precisely, let α be an arbitrary real root of a quadratic equation with integer coefficients; say, . Given any rational number 0 < x < 1 (say, x = 1/2) and any positive integer n, we count the number of elements of the sequence α, 2α, 3α, ..., modulo 1 that fall into the subinterval [0, x]. We prove that this counting number satisfies a central limit theorem in the following sense. First, we subtract the “expected number” nx from the counting number, and study the typical fluctuation of this difference as n runs in a long interval 1 ≤ nN. Depending on α and x, we may need an extra additive correction of constant times logarithm of N; furthermore, what we always need is a multiplicative correction: division by (another) constant times square root of logarithm of N. If N is large, the distribution of this renormalized counting number, as n runs in 1 ≤ nN, is very close to the standard normal distribution (bell shaped curve), and the corresponding error term tends to zero as N tends to infinity. This is the main result of the paper (see Theorem 1.1).

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Abstract

Using fixed point methods, we prove the generalized Hyers–Ulam stability of homomorphisms in multi-C ternary algebras and of derivations on multi-C ternary algebras for the additive functional equation

e1

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If we have two information production processes with the same h-index, random removal of items causes one system to have a higher h-index than the other system while random removal of sources causes the opposite effect. In a Lotkaian framework we prove formulae for the h-index in case of random removal of items and in case of random removal of sources. In conclusion, we warn for the use of the h-index in case of incomplete data sets.

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The aim of this paper is to prove some common fixed point theorems under certain strict contractive conditions for mappings sharing the common property (E.A) in Menger spaces. As applications to our results, we obtain the corresponding common fixed point theorems under strict contraction in metric spaces. Thus, our results generalize many known results in Menger as well as metric spaces. Some related results are also derived besides presenting several illustrative examples.

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Abstract

If is a system of infinite sets, |AB|<r for (r<ω) then has a conflict free coloring with ω colors, i.e., a function so that each has a color i<ω with |F −1(i)∩A|=1.

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Abstract

We study the thermoelastic system in a domain with moving boundary, which was obtained when, instead of the Fourier’s law for the heat flux relation, we followed the linearized model proposed by Coleman and Gurtin [3] and Gurtin and Pipkin [6] about the memory theory of heat conduction. We show the existence, uniqueness and exponential decay rate of global regular solutions.

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Properties of Fourier–Haar coefficients of continuous functions are studied. It is established that Fourier–Haar coefficients of continuous functions are monotonic in a certain sense for convex functions. Questions of quasivariation of Fourier–Haar coefficients of continuous functions are also considered.

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A generalized Cauchy problem for almost linear hyperbolic functional differential systems is considered. A theorem on the global existence of classical solutions is proved. It is shown a result on the differentiability of solutions with respect to initial functions. A method of characteristics and integral functional inequalities are used.

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Let S be a foundation locally compact topological semigroup, and let M a(S) be the space of all measures μM(S) for which the maps x↦|μ|∗δ x and x↦|μ|∗δ x from S into M(S) are weakly continuous. The purpose of this article is to develop a notion of character amenability for semigroup algebras. The main results concern the χ-amenability of M a(S). We give necessary and sufficient conditions for the existence of a left χ-mean on M a(S).

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We investigate the existence and properties of solutions for a class of systems of Dirichlet problems involving the perturbed phi-Laplace operators. We apply variational methods associated with the Fenchel conjugate. Our results cover both sublinear and superlinear cases of nonlinearities.

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We study the singularities of Galilean distance and Galilean height functions intrinsically related to Frenet frame along a curve embedded into Galilean space. We establish the relationships between singularities of the functions and geometric invariants under the action of Galilean group of curves which are deeply related to the order of contact with Galilean helices.

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It is shown that Sturm theorems, formulated in the 1830’s ([1], [2], [3] and [4]) and valid for second order linear homogeneous differential equation L(y)≡y″+a(x)y′+b(x)y=0, could as well be formulated for the class of nonhomogeneous linear differential equations L(y)=f(x). Criteria for the existence of oscillatory solutions of nonhomogeneous equations, as well as more exact locations of the zeros are given.

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We define ζμ-sets, (ζ,μ)-closed sets and generalized ζμ-sets in a generalized topological space and investigate properties of several low separation axioms of generalized topologies constructed by the families of these sets. Characterizations of some properties of (ζ,μ)-R 0 and (ζ,μ)-R 1 generalized topological spaces will be given.

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Abstract

Title of an article can be descriptive, declarative or a question. It plays important role in both marketing and findability of article. We investigate the impact of the type of article titles on the number of citations and downloads articles receive. Number of downloads and citations for all articles published in six of PLoS (Public Library of Science) journals (2,172 articles) were obtained from PLoS and type of each article's title (including descriptive, indicative and question) was determined as well as the number of substantive words in title (title length). Statistical difference and correlation tests were carried out. The findings showed that differences exist between articles with different types of titles in terms of downloads and citations, especially articles with question titles tended to be downloaded more but cited less than the others. Articles with longer titles were downloaded slightly less than the articles with shorter titles. Titles with colon tended to be longer and receive fewer downloads and citations. As expected, number of downloads and citations were positively correlated.

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The notion of generalized submaximal spaces is introduced and studied. Properties and characterizations of generalized submaximal spaces are discussed.

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The Hodge–de Rham Theorem is introduced and discussed. This result has implications for the general study of several partial differential equations. Some propositions which have applications to the proof of this theorem are used to study some related results concerning a class of partial differential equation in a novel way.

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Abstract

Let f: RR be integrable in a neighbourhood of xR. If there are real numbers α 0,α 2,…,α 2n−2 such that

ea
exists for some δ>0 then the limit is called the 2n-th symmetric Laplace derivative at x. There is a corresponding definition of (2n+1)-th symmetric Laplace derivative. It is shown that this derivative is a generalization of the symmetric d.l.V.P. derivative. Some properties of this derivative are studied.

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This paper studies the production of dissertations in eight research fields in the natural sciences, the social sciences and the humanities. In using doctoral dissertations it builds on De Solla Prices seminal study which used PhD dissertations as one of several indicators of scientific growth (Price, Little science, big science, ). Data from the ProQuest: Dissertations and Theses database covering the years 1950–2007 are used to depict historical trends, and the Gompertz function was used for analysing the data. A decline in the growth of dissertations can be seen in all fields in the mid-eighties and several fields show only a modest growth during the entire period. The growth profiles of specific disciplines could not be explained by traditional dichotomies such as pure/applied or soft/hard, but rather it seems that the age of the discipline appears to be an important factor. Thus, it is obvious that the growth of dissertations must be explained using several factors emerging both inside and outside academia. Consequently, we propose that the output of dissertations can be used as an indicator of growth, especially in fields like the humanities, where journal or article counts are less applicable.

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Abstract

We consider sequences of functions that have in some sense a universal distribution of limit points of zeros in the complex plane. In particular, we prove that functions having universal approximation properties on compact sets with connected complement automatically have such a universal distribution of limit points. Moreover, in the case of sequences of derivatives, we show connections between this kind of universality and some rather old results of Edrei/MacLane and Pólya. Finally, we show the lineability of the set what we call Jentzsch-universal power series.

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Abstract

In the current scenario of the global economy and race for the next Asian super power, overall economic strength of the two countries, India and China, is a most debated topic. The future role of intellectual property protection especially in the form of patent system and the growth of industrialization for these two developing economies in ASIA may prove to be crucial over all other assets. In the current development scene of the changing global market supported by intangible asset of inventions protected mainly through the patents is emerging to play an important role. This paper elaborates the statistical research on patents granted/filed in the US Patent and Trade Mark office (US-PTO), PCT of WIPO and in the home countries over last 35 years of aforesaid two Asian countries. It is found that the economic and technological growth of both of the countries may make main difference primarily based on the level of patenting activity by them.

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Abstract

Bibliographic databases are frequently used and analysed for the purpose of assessing the capacity and performance of individual researchers or entire research systems. Many of the advantages and disadvantages are the subject of continued discussion in the relevant literature, although only rarely with respect to the regional dimension of scientific publication activity. The importance of the regional dimension of science is reflected in many theoretical concepts, ranging from innovation system theories to territorial cluster concepts and learning regions. This article makes use of the extensive information found in bibliographic data and assesses the reliability of this information as a proxy indicator for the spatial dimension of scientific collaboration in emerging economies. This is undertaken using the example of the emerging field of biotechnology in China from 2000 onwards. Two data sets have been prepared: (1) the frequently used ISI Web of Knowledge database (SCI-Expanded) and (2) the domestic Chinese Chongqing VIP database. Both data sources were analysed using a variety of bibliometric and network scientific methods. The structural and topological similarity of networks, built from co-authorship data, is apparent between the two databases. At an abstract level, general network forces are present, resulting in similar network sizes, clustering, or assortativity. However, introducing additional complexity through regional subdivision reveals many differences between the two data sources that must be accounted for in the analytic design of future scientometric research in dynamic spaces.

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Authors: Pedro Albarrán, Juan A. Crespo, Ignacio Ortuño and Javier Ruiz-Castillo

Abstract

This paper studies evidence from Thomson Scientific (TS) about the citation process of 3.7 million articles published in the period 1998–2002 in 219 Web of Science (WoS) categories, or sub-fields. Reference and citation distributions have very different characteristics across sub-fields. However, when analyzed with the Characteristic Scores and Scales (CSS) technique, which is replication and scale invariant, the shape of these distributions over three broad categories of articles appears strikingly similar. Reference distributions are mildly skewed, but citation distributions with a 5-year citation window are highly skewed: the mean is 20 points above the median, while 9–10% of all articles in the upper tail account for about 44% of all citations. The aggregation of sub-fields into disciplines and fields according to several aggregation schemes preserve this feature of citation distributions. It should be noted that when we look into subsets of articles within the lower and upper tails of citation distributions the universality partially breaks down. On the other hand, for 140 of the 219 sub-fields the existence of a power law cannot be rejected. However, contrary to what is generally believed, at the sub-field level the scaling parameter is above 3.5 most of the time, and power laws are relatively small: on average, they represent 2% of all articles and account for 13.5% of all citations. The results of the aggregation into disciplines and fields reveal that power law algebra is a subtle phenomenon.

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Katy Börner: Atlas of science: visualizing what we know

The MIT Press, Cambridge, MA/London, UK, 2010, US$20

Author: Loet Leydesdorff
Open access