Evaluación de la Actividad Matemática: Algunos Números

Joaquín Ortega

Departamento de Matemáticas, IVIC y Escuela de Matemáticas, UCV

1 Aclaratoria Necesaria

En lo que sigue el lector no encontrará reflexiones sobre la naturaleza del trabajo matemático, ni ideas sobre su evaluación. Encontrará sólo números. Números que hablan sobre cosas que para los matemáticos son conocidas pero que parecen no serlo para científicos que trabajan en otras disciplinas. ¿Por qué, entonces, abundar sobre algo que sabemos? Daré mis razones.

Desde la introducción del Sistema de Promoción el Investigador (SPI) por el CONICIT, la comunidad científica nacional, y en particular la comunidad matemática, se enfrentó al problema de la evaluación de su actividad. En algunas instancias, por ejemplo en el IVIC a través de la Comisión Clasificadora, una parte de la comunidad ha sido evaluada de manera periódica desde mucho antes.

Esta evaluación se ha realizado por comisiones multidisciplinarias (Física, Química y Matemáticas en el SPI) que en muchos casos desconocen las características y naturaleza del trabajo matemático.

Por ejemplo, en Matemáticas la regla (con poquísimas excepciones) es que los autores de un trabajo se listen en orden alfabético. La idea de autores de distintas categorías (primer autor, segundo autor, etc.) es, prácticamente, desconocida. También es poco común que los trabajos que resultan de una tesis de doctorado tengan como coautor al tutor de la tesis. Por otro lado, es muy común que los trabajos sean difundidos en versiones preliminares a través de prepublicaciones de libre distribución, muchas veces años antes de que los resultados sean definitivamente publicados en una revista.

Las comisiones del SPI buscaron métodos de evaluación ‘objetivos’, lo que ellos parecen haber considerado sinónimo de numérico: uno o varios números que permitieran decidir sobre la ubicación de un investigador en una escala, y diseñaron un esquema de evaluación que esencialmente ‘cuenta’. En mayor o menor grado este espíritu parece haberse transmitido a otros sistemas de evaluación. La razón parece ser la falta de tiempo para hacer una evaluación más concienzuda del trabajo de nuestros colegas.

Desde la primera ronda del Programa de Promoción del Investigador muchos matemáticos se sintieron injustamente evaluados. En varias instancias este malestar se manifestó y se argumentó sobre sus causas, sobre lo inadecuado que pueden resultar parámetros pensados para otras disciplinas cuando son aplicados a Matemáticas, sobre la necesidad de hacer evaluaciones más profundas en casos atípicos o dudosos y sobre la inevitabilidad de introducir elementos subjetivos en el proceso de evaluación. Todas estas observaciones cayeron en oidos sordos. Lo único que se le solicitó a la AMV fue la elaboración de una lista un poco más amplia que la del Science Citation Index, de las revistas ‘buenas’ en Matemáticas, o al menos de aquellas en las cuales es ‘aceptable’ publicar, si queremos que estos trabajos sean considerados por la comisión del PPI. O sea, que no importa el trabajo en si sino el vehículo a través del cual se transmite.

Cansado de argumentar sobre lo que me parece un sistema básicamente injusto decidi buscar números que indiquen que lo que hemos dicho tantas veces es cierto: los matemáticos publicamos menos, publicamos trabajos más largos, con menos autores, que tardan más en aparecer y que son citados con menos frecuencia. Por supuesto, los números que siguen no ‘demuestran’ esto. Esa es una tarea casi imposible por las dimensiones de la base bibliografica que habria que revisar. Sin embargo, creo que indican claramente que esto es así. De cualquier manera, que el lector alcance su propia conclusión.

Mi posición personal es que los números nunca bastan. Que son necesarios, que son indicativos, pero que nada sustituye a la opinión (subjetiva) de expertos en el área. Y que es preferible correr el riesgo de la subjetividad que del sesgo instituido contra una disciplina.

2 La Comunidad Matemática Venezolana

2.1 ¿Cuántos matemáticos hay en Venezuela?

La respuesta a esta pregunta depende, por supuesto, de lo que definamos como matemático. El directorio mundial de la Unión Matemática Internacional (IMU) de 1994 tiene 54 matemáticos residenciados en Venezuela. Para poder ser incluido en el directorio es necesario haber publicado al menos dos artículos reseñados en Mathematical Reviews, Referativnyi Zhurnal o Zentralblatt für Mathematik en los cinco años anteriores. La lista es elaborada por la A.M.V. a solicitud de la IMU. En el directorio de 1998 aparecen 86 matemáticos residenciados en Venezuela.

Como comparación, en la base de datos de la AMV hay 361 personas, todas con un título de pregrado o de postgrado en Matemáticas.

Finalmente, usando la base de datos MathSciNet de la American Mathematical Society (ver apéndice) buscamos todos los autores residenciados en Venezuela que hubieran publicado al menos un artículo en el período 1995-98. En total obtuvimos 157 nombres de los cuales 41 habían publicado sólo en revistas nacionales. Estos datos se resumen en la siguiente gráfica

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100 200 300 400  ^{116}  ^{41}  ^{157}  ^{54}  ^{86}  ^{361}_{95-98}_{Pub. Int.}  _{95-98}_{Pub. Nac.}  _{95-98}_{Pub.}_{Nac + Int.} _{World}_{Directory}_{1994}  _{World}_{Directory}_{1998}  _{A.M.V.}

Figura 1

Matemáticos en Venezuela

La siguiente gráfica muestra la distribución por institución de los autores de artículos publicados en revistas internacionales, para los datos obtenidos por MathSciNet, mencionados anteriormente.

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_{USB} _{ULA} _{IVIC} _{LUZ} _{UDO} _{UCLA} _{UMET} _{UNA} 5 10 15 20 25 30 ^{30}  ^{29}  ^{22}  ^{11}  ^{11}  ^{7}  ^{4}  ^{1}  ^{1}

Figura 2

Autores en Venezuela con publicaciones en revistas internacionales en el período 1995-98 registradas en MathSciNet, clasificados por institución

2.2 ¿Cuánto publican?

A continuación mostramos el número de artículos publicados por autores residenciados en Venezuela para los años 1985 a 1998. Las publicaciones están discriminadas según la publicación sea nacional, latinoamericana o internacional. Los datos, de nuevo, son de MathSciNet.

En la gráfica se observa una tendencia ascendente del número de publicaciones hasta el año 93, hay un descenso en el 94 y luego, de nuevo, una tendencia ascendente, aunque sin alcanzar el nivel de 1993.

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Figura 3

Publicaciones de matemáticos residenciados en Venezuela según MathSciNet, clasificados según el origen de la revista, por año

Resulta interesante ver si el Sistema de Promoción del Investigador ha tenido algún efecto apreciable sobre la producción de artículos científicos en revistas internacionales en el área de Matemáticas. Teniendo en cuenta que la primera convocatoria se realizó en marzo de 1990 sus efectos no pueden estar presentes antes del siguiente año. Por lo tanto dividimos los datos en dos períodos: 85-91 y 91-98 y realizamos regresiones para los datos correspondientes así como para la serie completa. Los resultados se muestran en la Figura 4.

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^{85-91}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.} ^{91-97}

Figura 4

Publicaciones en revistas internacionales por matemáticos

en Venezuela según MathSciNet, por año

Las pendientes obtenidas fueron 5,54 art./año para la primera serie y 1,68 para la segunda mientras que la serie total tiene pendiente 3,56. Como se observa hay una diferencia significativa entre ambos períodos.

Por último, exploramos la evolución del número de artículos publicados en Acta Científica Venezolana, para el mismo período de tiempo. Los datos se presentan en la Figura 5. Se observa un año atípico, 1987, en el cual hay 24 artículos publicados. Esto se debe, en parte, a que ACV dedicó un número especial al X aniversario del postgrado en Matemáticas de la UCV, en el cual se incluyeron 13 artículos de Matemáticas.

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85 86 87 88 89 90 91 92 93 94 95 96 97 98 5 10 15 20 25 ^{3}  ^{8}  ^{24}  ^{3}  ^{5}  ^{1}  ^{3}  ^{5}  ^{3}  ^{0}  ^{2}  ^{1}  ^{2}  ^{3}

Figura 5

Artículos de Matemáticas publicados en Acta Científica Venezolana, por año

3 Las Publicaciones Matemáticas en el Science Citation Index

El Institute for Scientific Information (ISI) es una compañía privada, fundada en 1958 por Eugene Garfield, dedicada al mantenimiento y publicación de una base de datos sobre publicaciones científicas. Una de sus publicaciones más conocidas es el Science Citation Index (SCI), que trae información bibliográfica sobre citas a artículos producidas en los ‘core journals’. En la actualidad cubre aproximadamente 3500 publicaciones periódicas en más de 150 disciplinas. Más información sobre el ISI y sus productos puede obtenerse en la red (http://www.isinet.com).

El ISI ha producido una serie de índices que pretenden medir diversos aspectos de la actividad científica y, en particular, de las publicaciones. A continuación consideramos algunos de ellos, aunque debemos aclarar que, a nuestro entender, no está muy claro que es lo que realmente miden.

3.1 El Factor de Impacto (Impact Factor)

El Institute for Scientific Information, define el factor de impacto (Impact Factor) de una publicación periódica de la siguiente manera:

‘El factor de impacto de una publicación periódica es una medida de la frecuencia con la cual el “artículo promedio” en la publicación ha sido citado en un año particular...

El factor de impacto se calcula dividiendo el número de citas recibidas (en el año en cuestión) a artículos publicados en los dos años anteriores entre el número total de artículos publicados en los dos años anteriores...’

Ejemplo: Si la revista A publica 100 artículos entre 1993 y 1994 y recibe 500 citas a esos artículos en el año 1995, su factor de impacto para 1995 es 5.

A continuación presentamos una gráfica con el factor de impacto por área para el período comprendido entre 1981 y 1992, agrupando todas las revistas monitoreadas por el Science Citation Index. Los datos están tomados de la publicación Science Watch del ISI. En la primera columna se presentan los datos en valores absolutos mientras que en la segunda se presentan normalizados según el valor para Matemáticas.

Inmunología 15.59 5.34 Biol. Molecular 14.78 5.06 Neurología 12.28 4.20 Biología y Bioquím. 11.69 4.00 Astronomía 10.40 3.56 Farmacología 7.66 2.62 Med. Clínica 6.64 2.27 Física 6.44 2.21 Geociencias 6.36 2.18 Química 6.04 2.07 Ecol. y Ambien. 4.99 1.71 Botan. y Zool. 4.21 1.44 Computación 3.09 1.06 Agricultura 3.09 1.06 C. Materiales 3.01 1.03 Matemáticas 2.92 1.00 Ingeniería 2.63 0.90

Figura 6

Factor de impacto por área para el período 1981-92 en todo el mundo

Resultados similares se observan para el factor de impacto por área para las publicaciones producidas en USA y el Reino Unido. Estos datos, tomados como dijimos de Science Watch, presentan un promedio para todos los artículos publicados en el período en cuestión y revisados por el ISI. Para un año particular, en nuestro caso 1995, es posible obtener el factor de impacto por revista y esto permite tener una mejor idea de la distribución de este factor por área.

La siguiente gráfica presenta el Factor de Impacto Promedio para las revistas incluidas en la base de datos del Science Citation Index por área, para el año 1995. Para la presentación hemos escogido una versión del ’boxplot’ o diagrama de caja, en la cual hemos eliminado los extremos superiores en aquellos casos en los cuales los valores se salen de la escala. En el apéndice incluimos las tablas de valores correspondientes. El valor medio se representa por el símbolo •, mientras que la mediana está representada por ⊗. Los lados inferior y superior del rectángulo o caja son el primer y tercer cuartil, respectivamente, de modo que dentro de la caja se encuentra el 50% central de los datos. Los extremos superior e inferior del conjunto de datos se representan por los símbolos ⊤ y ⊥, respectivamente.

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1 2 3  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.} ⊥ • ⊗_{Bioquímica}⊥ • ⊗_{Biol. Celular}⊥ • ⊗_{Virología} ⊥ • ⊗_{Biofísica} ⊥ • ⊗_{Microbiol.} ⊥ • ⊗_{Química} ⊥ • ⊗_{Física} ⊥ • ⊗_{Biología} ⊥ • ⊗ ⊤_{Estadística} ⊥ • ⊗ ⊤_{Comput.} ⊥ • ⊗ ⊤_{Mat. Apl.} ⊥ • ⊗ ⊤_{Matemáticas}

Figura 7

Factor de Impacto Promedio para las revistas incluidas en la lista del SCI para 1995

3.2 El Indice de Inmediatez (Inmediacy Index)

De nuevo, el Institute for Scientific Information define el índice de inmediatez de una publicación periódica de la siguiente manera:

“El índice de inmediatez de una publicación periódica es una medida de la rapidez con la cual es citado el “artículo promedio” en la publicación ...

El índice de inmediatez se calcula dividiendo el número de citas recibidas en el año a artículos publicados en el mismo año entre el número de artículos publicados en el año.”

Ejemplo: Si la revista A publica 50 artículos en 1995 y recibe 100 citas a esos artículos en ese año, su índice de inmediatez para 1995 es 2.

La Figura 8 muestra el índice de inmediatez promedio para las revistas incluidas en la base de datos del SCI por área, para el año 1995.

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.1 .2 .3 .4 .5 .6 .7  ⊥ • ⊗_{Bioquímica}⊥ • ⊗_{Biol. Celular}⊥ • ⊗_{Virología} ⊥ • ⊗_{Biofísica} ⊥ • ⊗_{Biología} ⊥ • ⊗_{Física} ⊥ • ⊗_{Microbiol.} ⊥ • ⊗_{Química} ⊥ • ⊗_{Comput.} ⊥ • ⊗_{Estadística} ⊥ • ⊗ ⊤_{Mat. Apl.} ⊥ • ⊗ ⊤_{Matemáticas}

Figura 8

Índice de Inmediatez Promedio para las revistas incluidas en la lista del SCI para 1995

3.3 Vida media de citas recibidas (Cited Half-Life)

El Institute for Scientific Information define la vida media de citas recibidas de una publicación periódica de la siguiente manera:

“La vida media de las citas recibidas es el número de años de publicación, a partir del año en cuestión, que reflejan el 50% de las citas recibidas en el año en cuestión. ... Sólo se calcula para publicaciones con 100 o más citas.”

Ejemplo: Una vida media de 5 años para una revista en 1995 indica que al menos la mitad de las citas recibidas ese año corresponden a artículos publicados por la revista en los 5 años precedentes. La vida media se mide en años y sólo se registra el valor si es menor que 10. Las revistas que tienen vida media mayor a 10 años se agrupan en una categoría. Por lo tanto, el porcentaje de revistas con vida media en esta categoría entre la lista de revistas que considera el SCI puede considerarse como una medida de la ‘longevidad’ promedio de los artículos del área.

La Figura 9 presenta el porcentaje de revistas con vida media superior a 10 años para revistas en el SCI.

Matemáticas 68.16 Estadística 53.85 Química 35.29 Biología 34.00 Ingeniería 25.00 Física Mat. 18.75 Física 17.86 Computación 11.76 Biofísica 11.43 Microbiología 8.47 Bioquímica 8.29 Biología Cel. 2.06 Virología 0.00

Figura 9

Porcentaje de las revistas en la lista del SCI con vida media mayor o igual a 10 años, clasificadas por área

4 Comparación de Revistas

Hay ciertas características de las publicaciones que no se ven reflejadas en los datos que almacena el ISI. Por esta razón, y con el objetivo de comparar las publicaciones matemáticas y la productividad en esta área con otras, seleccionamos algunas publicaciones entre los primeros lugares de la lista según el Factor de Impacto del ISI. Buscamos revistas que publicaran artículos de investigación (no de revisión) y que tuviesen un tamaño razonable para tratar de hacer una revisión exhaustiva.

Si bien el objetivo inicial fue hacer esta comparación para una cantidad importante de áreas, de modo de poder estudiar semejanzas y diferencias, la dificultad y el tiempo necesario para ello hicieron que nos limitaremos a tres: Física Matemáticas y Química.

Las revistas seleccionadas fueron las siguientes (entre paréntesis indicamos el lugar que ocuparon el año 1995 en la lista del SCI según el factor de impacto y el país/continente de publicación): En Física, Physical Review Letters (2, USA), Europhysics Letters (8, Europa) y Annals of Physics (11, USA). En Matemáticas: Acta Mathematica (1, Suecia), Annals of Mathematics (5, USA), Communications in Pure and Applied Mathematics (7, USA) Inventiones Mathematicae (6, Alemania), Sbornik (2, Rusia) y en Química, Journal of the American Chemical Society (5, USA), Angewandte Chemie International Edition (3, Alemania), Chemistry (^{1} , Europa) y Journal of Computacional Chemistry (7, USA).

1Esta revista comenzó a publicarse en 1995 y apareció junto con Angewandte Chemie Int.

Ed. hasta 1996. No está en la lista del SCI pero la incluimos porque no costaba más trabajo revisarla.

Para las revistas seleccionadas hicimos un estudio completo de los volúmenes publicados durante el año 1995 que incluyó: Número de artículos publicados, autores por artículo y páginas por artículo. El Journal of the American Chemical Society tiene dos secciones, Comunicaciones y Artículos, que son presentadas por separado en las gráficas y tablas.

Las gráficas para los resultados obtenidos se presentan a continuación. Las tablas correspondientes se presentan en el apéndice. En algunos casos los valores máximos o la media no aparecen en la gráfica, por problemas de escala. En estos casos recomendamos ver los valores que aparecen en las tablas.

La primera gráfica muestra el número de páginas por artículo.

._{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.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10 20 30 40 50 60 70 80 90 100 110 120 130 140  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.} ⊥ • ⊗ ⊤_{Acta Math}⊥ • ⊗ ⊤_{Sbornik} ⊥ • ⊗ ⊤_{Ann Math}⊥ • ⊗ ⊤_{C P&A M}⊥ • ⊗ ∧_{Inv Math} ⊥ • ⊗ ⊤_{Ann Phys} ⊥ • ⊗ ⊤_{Eur Let} ⊥ • ⊗ ⊤_{PhysRevLet}⊥ • ⊗ ⊤_{JCC} ⊥ • ⊗ ⊤_{JACS-Art}⊥ • ⊗ ⊤_{JACS-Com}⊥ • ⊗ ⊤_{JACS-Todo}⊥ • ⊗ ⊤_{Ang Chem}⊥ • ⊗ ⊤_{Chem}

Figura 10

Páginas por artículo

La siguiente gráfica presenta el número de autores por artículo. Para las revistas de Física y Química (excepto Annals of Physics y Journal of Computational Chemistry) los valores máximos no aparecen en la gráfica. Tampoco aparece el valor medio (12.28) para Physical Review Letters.

Hacemos la observación de que entre las revistas de Matemática hay un sólo artículo con cinco autores (en Annals of Mathematics) y ninguno con cuatro. Todos los demás tienen a lo sumo tres autores y la gran mayoría (75% para todas las revistas) tiene dos o menos. De hecho, para dos revistas, Sbornik e Inventiones Mathematicae, 75% de los artículos tienen un sólo autor

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1 2 3 4 5 6 7 8  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.} ⊥ • ⊗ ⊤_{Acta Math}⊥ • ⊗ ⊤_{Sbornik} ⊥ • ⊗ ⊤_{Ann Math}⊥ • ⊗ ⊤_{C P&A M}⊥ • ⊗ ⊤_{Inv Math} ⊥ • ⊗ ⊤_{Ann Phys} ⊥ • ⊗_{Eur Let} ⊥ ⊗_{PhysRevLet}⊥ • ⊗ ⊤_{JCC} ⊥ • ⊗_{JACS-Art}⊥ • ⊗_{JACS-Com}⊥ • ⊗_{JACS-Todo}⊥ • ⊗_{Ang Chem}⊥ • ⊗_{Chem}

Figura 11

Autores por artículo

A continuación presentamos el número de páginas por autor para las revistas revisadas durante el año 1995.

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10 20 30 40 50 60 70 80 90 100 110  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.} ⊥ • ⊗ ⊤_{Acta Math}⊥ • ⊗ ⊤_{Sbornik} ⊥ • ⊗ ⊤_{Ann Math}⊥ • ⊗ ⊤_{C P&A M}⊥ • ⊗ ⊤_{Inv Math} ⊥ • ⊗ ⊤_{Ann Phys} ⊥ • ⊗ ⊤_{Eur Let} ⊥ • ⊗ ⊤_{PhysRevLet}⊥ • ⊗ ⊤_{JCC} ⊥ • ⊗ ⊤_{JACS-Art}⊥ • ⊗ ⊤_{JACS-Com}⊥ • ⊗ ⊤_{JACS-Todo}⊥ • ⊗ ⊤_{Ang Chem}⊥ • ⊗ ⊤  _{Chem}

Figura 12

Páginas por autor

Otro parámetro que quisimos investigar fue el tiempo para publicación de un artículo en las distintas revistas consideradas. Dada la cantidad de artículos en las revistas de las ciencias experimentales (más de 1100 en Physical Review Letters, por ejemplo) tomamos al azar una muestra reducida de artículos para obtener estos datos. Esa muestra se usó también para estudiar a los autores en relación a los parámetros que presentamos en la próxima sección. Los tamaños de las muestras por revista fueron los siguientes: Physical Rev. Lett. (20), Europhysics Letters (30), Annals of Physics (10), JACS Comm. (15), JACS Art. (15), Angewandte Chemie (25), Chemistry (10), J. Computacional Chemistry (15). En este sentido sería deseable ampliar el tamaño de las muestras para tener una mayor precisión.

Para las revistas de matemáticas revisamos todos los artículos publicados en 1995 salvo que para Sbornik encontramos una serie de contradicciones (para varios artículos la fecha de recepción era posterior a la de publicación) y por ello no la incluimos.

El tiempo para publicación lo medimos como el tiempo transcurrido desde la recepción del artículo por los editores hasta el primer día del período de publicación (semana, mes, trimestre, etc.) del número en el cual apareció el artículo, en días.

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100 200 300 400 500 600 700 800 900 1000 1100 1200 1300  _{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  _{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}_{.}  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^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{.}^{1 año}^{2 años}^{3 años} ⊥ • ⊗ ⊤_{Acta Math}⊥ • ⊗ ⊤_{Ann Math}⊥ • ⊗ ⊤_{C P&A M}⊥ • ⊗ ⊤_{Inv Math} ⊥ • ⊗ ⊤_{Ann Phys} ⊥ • ⊗ ⊤_{Eur Let} ⊥ • ⊗ ⊤_{PhysRevLet}⊥ • ⊗ ⊤_{JCC} ⊥ • ⊗ ⊤_{JACS-Art}⊥ • ⊗ ⊤_{JACS-Com}⊥ • ⊗ ⊤_{JACS-Todo}⊥ • ⊗ ⊤_{Ang Chem}⊥ • ⊗ ⊤_{Chem}

Figura 13

Tiempo para publicación de un artículo, en días

5 Comparación de Autores

Como parte de este estudio sobre las características del trabajo matemático y de las publicaciones en esta área, buscamos también alguna medida de la productividad en las distintas áreas. Nuestro objetivo era revisar la productividad de los autores de los artículos en las revistas consideradas.

En concreto nos planteamos considerar uno de los autores de cada artículo revisado en la sección anterior. Este sería el primer autor para los artículos de las ciencias experimentales, mientras que para Matemáticas, donde lo usual es ordenar los autores alfabéticamente, tomamos uno al azar. La cantidad de artículos publicados por año en las revistas de Física y Química consideradas nos hizo reducir el objetivo a una muestra por cada revista.

Para las revistas de Matemáticas consideramos al menos un autor por artículo y usamos la base de datos MathSciNet para obtener los datos relevantes, de modo que la información en esta área es exhaustiva para los artículos considerados. Contamos los artículos de investigación listados en la base de datos para el autor (en la medida de lo posible desechamos artículos de revisión y divulgación) y dividimos entre el lapso transcurrido desde la primera hasta la última publicación.

Para las revistas de Física y Química no teníamos a mano una base de datos como MathSciNet que nos permitiera estudiar la producción global de los autores. En consecuencia, para Física revisamos los artículos publicados en los años 1995 y 1996 para los primeros autores de los artículos seleccionados en la muestra mencionada en la sección anterior, según Physics Abstracts. Para Química, revisamos las publicaciones de 1995 según Chemical Abstracts. Los resultados se muestran en la siguiente gráfica.

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Figura 14

Promedio de publicaciones por año por autor

Como dato curioso, entre los autores incluidos en las revistas matemáticas esta A. Wiles, ya que el artículo donde se demuestra el Ultimo Teorema de Fermat fue publicado en Annals of Mathematics en 1995. También hay varios ganadores de la Medalla Fields.

Finalmente revisamos las publicaciones por año para una muestra de ganadores del Premio Nobel en Física y Química y de la Medalla Fields en Matemáticas, dado que no existe Premio Nobel. Estos premios no tienen exactamente las mismas características (ver apéndice), pero sin embargo nos parece que la comparación resulta válida.

Consideramos 22 ganadores de la medalla Fields (Borcherds, Gowers, Kontsevich, McMullen, Zelmanov, Yoccoz, Lions, Bourgain, Drinfeld, Jones, Mori, Witten, Donaldson, Faltings, Freedman, Connes, Thurston, Yau, Deligne, Fefferman, Margulis, Quillen) 13 ganadores del Nobel en Física (Charpak, Chu, Cohen-Tannoudji, de Gennes, Friedmann, Hulse, Laughlin, Lee, Osheroff, Phillips, Reines, Stormer, Tsui) y 12 de Química (Boyer, Rowland, Crutzen, Skou, Walker, Corey, Ernst, Marcus, Mullis, Olah, Rowlando, Smalley). Para los primeros revisamos su trayectoria completa usando MathSciNet. Para los segundos revisamos los artículos publicados en 1985, 1990 y 1995 según Physics Abstracts, mientras que para los últimos revisamos la producción en los períodos 77-81, 82-86 y 87-91 según los compendios quinquenales de Chemical Abstracts. Los resultados se muestran en la gráfica 14.

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Figura 15

Promedio de publicaciones por año para ganadores del premio Nobel o de la Medalla Fields

Finalmente usamos el Science Citation Index para ver el número de citas recibidas durante 1995 por 8 Premios Nobel en Química, 9 en Física y 13 ganadores de la Medalla Fields. Los resultados se presentan en la Figura 16.

Como detalle interesante, para el momento en que se realizó el foro (marzo de 1999) ninguno de los ganadores de la Medalla Fields en 1998, ni el ganador de la Medalla Nevalinna para el mismo año, ni dos de los ganadores de la Medalla Fields en 1994 clasificarían según los criterios del PPI al nivel III.

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Figura 16

Citas durante 1995 para ganadores del premio Nobel o de la Medalla Fields

6 Apéndice

6.1 MathSciNet

Existen varias publicaciones periódicas dedicadas a revisión de artículos matemáticos: Zentralblatt für Mathematik und ihre Grenzgebiete (Zbl), Mathematical Reviews y Refetarinik Zhurnal. La más antigua de ellas es Zbl, que comenzó a publicarse en 1931 en Alemania con Otto Neugebauer como editor. Como resultado de las políticas discriminatorias del régimen nacional-socialista en Alemania en los 30, se le prohibió a muchos matemáticos hacer revisiones para Zbl y la American Mathematical Society decidió iniciar la publicación de Mathematical Reviews en 1940. El primer editor fue, de nuevo, Otto Neugebauer, quien para entonces trabajaba en Brown University. Hoy en día, más de 10.000 matemáticos sirven de revisores y todo el material desde 1940 esta incorporado en la base de datos, en línea desde 1996. Los productores revisan anualmente más de 100.000 artículos o monografías provenientes 10.000 números de revistas, monografías y colecciones, de los cuales seleccionan unos 65.000 para ser revisados. Prácticamente todas las publicaciones matemáticas referadas son revisadas e incorporadas a la base de datos, por lo que la información disponible en ella sobre publicaciones es bastante exhaustiva y altamente confiable.

6.2 Las Medallas Fields

En el Congreso Mundial de Matemáticos de 1924, realizado en Toronto, Canada, se decidió que en cada Congreso Mundial se otorgarían dos medallas para reconocer logros sobresalientes en Matemáticas. El Prof. J. D. Fields, un matemático canadiense que era secretario de la Unión Matemática Internacional, donó el dinero para establecer las medallas, que recibieron su nombre. De acuerdo al deseo de Fields de que los premios reconociesen tanto el trabajo realizado como el potencial futuro, se acordó restringir las medallas a matemáticos que no hubiesen pasado de cuarenta años el año del congreso.

En 1966 se acordó que, dada la expansión de la investigación matemática, hasta cuatro medallas se podrían otorgar en cada congreso. Hasta la fecha los galardonados han sido: 1936 Lars Valerian AHLFORS, Jesse DOUGLAS. 1950 Laurent SCHWARTZ, Atle SELBERG. 1954 Kunihiko KODAIRA, Jean-Pierre SERRE. 1958 Klaus Friedrich ROTH, René THOM. 1962 Lars HÖRMANDER, John Willard MILNOR. 1966 Michael Francis ATIYAH, Paul Joseph COHEN,

Alexander GROTHENDIECK, Stephen SMALE. 1970 Alan BAKER, Heisuke HIRONAKA,

Serge NOVIKOV, John Griggs THOMPSON. 1974 Enrico BOMBIERI, David Bryant MUMFORD. 1978 Pierre René DELIGNE, Charles Louis FEFFERMAN,

Gregori Alexandrovitch MARGULIS, Daniel G. QUILLEN. 1982 Alain CONNES, William P. THURSTON, Shing-Tung YAU. 1986 Simon K. DONALDSON, Gerd FALTINGS, Michael H. FREEDMAN. 1990 Vladimir DRINFELD, Vaughan F.R. JONES,

Shigefumi MORI, Edward WITTEN. 1994 Jean BOURGAIN, Pierre-Louis LIONS,

Jean-Christophe YOCCOZ, Efim ZELMANOV. 1998 Richard E. BORCHERDS, W. Timothy GOWERS,

Maxim KONTSEVICH, Curtis T. MCMULLEN.

Andrew J. WILES (Special Tribute)

6.3 Tablas

Area  Mínimo Q1 Media Mediana Q3 Máximo
Bioquímica  0.21 0.98  3.30  1.88 3.65  44.41
Biol. Celular  0.21 1.06  3.30  1.81 3.24  40.48
Virología  0.10 1.24  2.17  1.63 3.12  6.03
Biofísica  0.21 0.62  2.05  1.42 2.57  12.11
Microbiología  0.02 0.76  2.21  1.47 2.39  22.10
Química  0.03 0.30  1.53  0.62 1.35  31.00
Física  0.00 0.31  1.47  0.64 1.64  19.41
Biología  0.00 0.29  1.47  0.91 2.00  13.40
Estadística  0.00 0.27  0.61  0.47 0.84  1.93
Computación  0.01 0.26  0.49  0.39 0.64  1.58
Mat. Aplicadas  0.00 0.28  0.48  0.41 0.62  1.62
Matemáticas  0.00 0.21  0.41  0.32 0.47  1.97

Tabla 1 Índice de Impacto Promedio para las revistas incluidas en la lista del SCI para 1995, por área

Area  Mínimo Q1 Media Mediana Q3 Máximo
Bioquímica  0 0.12  0.45  0.25 0.48  7.37
Biol. Celular  0 0.10  0.45  0.23 0.43  7.37
Virología  0 0.14  0.39  0.29 0.41  2.00
Biofísica  0 0.10  0.34  0.21 0.41  1.35
Biología  0 0.04  0.30  0.23 0.36  2.35
Física  0 0.06  0.27  0.14 0.33  1.62
Microbiología  0 0.09  0.23  0.14 0.26  1.55
Química  0 0.06  0.23  0.13 0.26  1.59
Computación  0 0.00  0.13  0.07 0.13  2.35
Estadística  0 0.01  0.12  0.06 0.17  0.80
Mat. Aplicadas  0 0.04  0.09  0.08 0.12  0.33
Matemáticas  0 0.02  0.07  0.05 0.09  0.36

Tabla 2 Índice de Inmediatez promedio para las revistas incluidas en la lista del SCI para 1995, por área

Revista  Mínimo Q1 Media Mediana Q3 Máximo
Acta Math.  14 27.75 43.25  33 53.25  94
Sbornik  6 12  19.53  18 24  46
Ann. Math.  10 20  37.97  33 46  109
Comm. P& A M  8 20  34.83  34 42  92
Inv. Math.  8 18  28.69  27 36  76
Ann. Phys.  4 18  31.78  27.5 39.25  133
Eur. Let.  4  6  5.98  6 6  8
Phys Rev Let  1  4  4.01  4 4  6
J. Comp. Chem.  1  8  12.73  11 16  28
JACS Arts.  3  6.25  8.92  8 11  32
JACS Comm.  1  2  2.01  2 2  4
JACS Todo  1  2  6.13  9 9  32
Ang. Chem.  1  3  3.11  3 3  5
Chemistry  3  5.25  8.36  7 9.75  28

Tabla 3 Páginas por artículo para las revistas para 1995 revisadas

Revista  Mínimo Q1 Media Mediana Q3 Máximo
Acta Math.  1  1  1.38  1  2  3
Sbornik  1  1  1.24  1  1  3
Ann. Math.  1  1  1.61  1  2  5
Comm. P& A M  1  1  1.9  2  2  3
Inv. Math.  1  1  1.24  1  1  3
Ann. Phys.  1  2  2.32  2  3  7
Eur. Let.  1  2  3.29  3  4  7
Phys Rev Let  1  2 12.18  3  5  452
J. Comp. Chem.  1  2  2.81  2  3  8
JACS Arts.  1  2  3.88  3  5  17
JACS Comm.  1  2  3.49  3  4  10
JACS Todo  1  2  3.72  3  5  17
Ang. Chem.  1  3  4.11  4  5  15
Chemistry  1  3  4.76  4  6  15

Tabla 4 Autores por artículo para las revistas revisadas durante el año 1995

Revista  Mínimo Q1 Media Mediana Q3 Máx.
Acta Math.  14  24.75 31.06  29 37.5  47
Sbornik  4  10.25  17.1  16 22  46
Ann. Math.  5  14  29.56  19.5 38.25 109
Comm. P& A M  4  11  19.87  18 23  66
Inv. Math.  4  13.5  22.62  18.5 29.5  76
Ann. Phys.  1.43  8.31 16.44  12.9 20  66.5
Eur. Let.  0.13  1.5  2.51  2  3  6
Phys Rev Let  0.01  0.8  1.41  1.33  2  5
J. Comp. Chem.  0.2  3  5.62  4.75  7.0  27
JACS Arts.  0.44  1.6  2.89  2.33  3.5  15
JACS Comm.  0.2  0.5  0.68  0.67  1  2
JACS Todo  0.2  0.67  1.98  1.33  2.67  15
Ang. Chem.  0.14  0.6  0.94  0.8  1  4
Chemistry  0.6  1.27  2.02  1.67  2.5  6

Tabla 5 Páginas por autor para las revistas revisadas durante el año 1995

Revista  Mínimo  Q1  Media Mediana  Q3  Máx.
Acta Math.  301 486.3  625.4  619 753.5  969
Ann. Math.  197 515  629.8  599 705.5 1271
Comm. P& A M  210 300  460.3  450 600  960
Inv. Math.  161 336.8  449.4  407.5 565.8 1230
Ann. Phys.  195 300.75  349  337.5 391  533
Eur. Let.  67 137  189.5  163.5 227  423
Phys Rev Let  96 134  245.3  195 285.5  686
J. Comp. Chem.  268 318.5  374.5  366 390.5  547
JACS Arts.  134 152  210.1  182 235  432
JACS Comm.  77 100  117.1  107 122  193
JACS Todo  77 107.5  163.6  144 188  432
Ang. Chem.  120 155  194.4  180 200  392
Chemistry  154 163.3  220  228 265  301

Tabla 6

Tiempo para publicación de un artículo para las revistas revisadas, en días, para artículos publicados en 1995

Revista  Mínimo Q1 Media Mediana Q3 Máximo
Acta Math.  0.55 1.32  2.21  1.64 2.38  9.75
Sbornik  0.13 0.74  1.29  1.15 1.56  4.21
Ann. Math.  0.4  1.11  1.87  1.56 1.87  10.43
C P&A M  0.17 1.31  2.26  2.0 2.65  6.81
Inv. Math.  0.25 1.14  1.73  1.71 2.21  4.22
Física  0.5  2.0  4.43  3.0 5.0  37.5
Química  1.0  2.0  5.47  4.0 7.0  24.0

Tabla 7 Promedio de publicaciones por año, por autor

Revista  Mínimo Q1 Media Mediana Q3 Máximo
Matemáticas  1.37 1.78  3.21  2.37 3.22  10.7
Física  2.0 3.66  6.15  4.66 8.0  16.0
Química  1.26 3.53  7.91  5.16 6.96  25.6

Tabla 8 Promedio de publicaciones por año para ganadores del premio Nobel o de la medalla Fields

Revista  Mínimo Q1  Media Mediana Q3 Máximo
Matemáticas  0  6  35.4  37 49  119.8
Física  7  21  250  43 75  1131
Química  50  123.8 425.8  268.5 587.5  788

Tabla 9 Citas en 1995 según el SCI para ganadores del premio Nobel o de la medalla Fields

Agradecimiento

El autor quiere agradecer la colaboración del Sr. Giovanny Meléndez de la Biblioteca Marcel Roche del IVIC por su colaboración en el uso de las bases de datos de la biblioteca.