9783030438616 - introduction to einstein's theory of relativity: from newton's attractive gravity to the repulsive gravity of vacuum energy (undergraduate texts in physics) de grøn, øyvind (33 resultados)
Idioma: Inglés
Editorial: Springer, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: GreatBookPrices, Columbia, MD, Estados Unidos de AmericaGreatBookPrices
Contactar con el vendedorVendedor de 5 estrellasCondición: Usado - Como Nuevo
EUR 42,61
Envío por EUR 2,31Se envía dentro de Estados Unidos de AmericaCantidad disponible: Más de 20 disponibles
Condición: As New. Unread book in perfect condition.
Idioma: Inglés
Editorial: Springer, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: GreatBookPrices, Columbia, MD, Estados Unidos de AmericaGreatBookPrices
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 48,84
Envío por EUR 2,31Se envía dentro de Estados Unidos de AmericaCantidad disponible: Más de 20 disponibles
Condición: New.
Idioma: Inglés
Editorial: Springer Nature Switzerland AG, CH, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: Rarewaves.com USA, London, LONDO, Reino UnidoRarewaves.com USA
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 51,23
Gastos de envío gratisSe envía de Reino Unido a Estados Unidos de AmericaCantidad disponible: Más de 20 disponibles
Paperback. Condición: New. Second Edition 2020. The revised and updated 2nd edition of this established textbook provides a self-contained introduction to the general theory of relativity, describing not only the physical principles and applications of the theory, but also the mathematics needed, in particular the calculus of di…fferential forms.Updated throughout, the book contains more detailed explanations and extended discussions of several conceptual points, and strengthened mathematical deductions where required. It includes examples of work conducted in the ten years since the first edition of the book was published, for example the pedagogically helpful concept of a "river of space" and a more detailed discussion of how far the principle of relativity is contained in the general theory of relativity. Also presented is a discussion of the concept of the 'gravitational field' in Einstein's theory, and some new material concerning the 'twin paradox' in the theory of relativity.Finally, the book contains a new section about gravitational waves, exploring the dramatic progress in this field following the LIGO observations.Based on a long-established masters course, the book serves advanced undergraduate and graduate level students, and also provides a useful reference for researchers.
Idioma: Inglés
Editorial: Springer, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: PBShop.store US, Wood Dale, IL, Estados Unidos de AmericaPBShop.store US
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 51,99
Gastos de envío gratisSe envía dentro de Estados Unidos de AmericaCantidad disponible: 3 disponibles
PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000.
Idioma: Inglés
Editorial: Springer, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: PBShop.store UK, Fairford, GLOS, Reino UnidoPBShop.store UK
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 47,67
Envío por EUR 6,85Se envía de Reino Unido a Estados Unidos de AmericaCantidad disponible: 3 disponibles
PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000.
Idioma: Inglés
Editorial: Springer, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: Ria Christie Collections, Uxbridge, Reino UnidoRia Christie Collections
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 40,15
Envío por EUR 13,99Se envía de Reino Unido a Estados Unidos de AmericaCantidad disponible: Más de 20 disponibles
Condición: New. In.
Idioma: Inglés
Editorial: Springer 2020-05, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: Chiron Media, Wallingford, Reino UnidoChiron Media
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 36,32
Envío por EUR 18,08Se envía de Reino Unido a Estados Unidos de AmericaCantidad disponible: 10 disponibles
PF. Condición: New.
Idioma: Inglés
Editorial: Springer, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: Brook Bookstore On Demand, Napoli, NA, ItaliaBrook Bookstore On Demand
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 47,83
Envío por EUR 6,80Se envía de Italia a Estados Unidos de AmericaCantidad disponible: 3 disponibles
Condición: new.
Idioma: Inglés
Editorial: Springer, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: GreatBookPricesUK, Woodford Green, Reino UnidoGreatBookPricesUK
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 39,30
Envío por EUR 17,51Se envía de Reino Unido a Estados Unidos de AmericaCantidad disponible: Más de 20 disponibles
Condición: New.
Idioma: Inglés
Editorial: Springer, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: Majestic Books, Hounslow, Reino UnidoMajestic Books
Contactar con el vendedorVendedor de 4 estrellasCondición: Nuevo
EUR 49,70
Envío por EUR 7,59Se envía de Reino Unido a Estados Unidos de AmericaCantidad disponible: 3 disponibles
Condición: New.
Idioma: Inglés
Editorial: Springer Nature Switzerland AG, Cham, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: Grand Eagle Retail, Bensenville, IL, Estados Unidos de AmericaGrand Eagle Retail
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 57,71
Gastos de envío gratisSe envía dentro de Estados Unidos de AmericaCantidad disponible: 1 disponibles
Paperback. Condición: new. Paperback. The revised and updated 2nd edition of this established textbook provides a self-contained introduction to the general theory of relativity, describing not only the physical principles and applications of the theory, but also the mathematics needed, in particular the calculus of differential… forms.Updated throughout, the book contains more detailed explanations and extended discussions of several conceptual points, and strengthened mathematical deductions where required. It includes examples of work conducted in the ten years since the first edition of the book was published, for example the pedagogically helpful concept of a "river of space" and a more detailed discussion of how far the principle of relativity is contained in the general theory of relativity. Also presented is a discussion of the concept of the 'gravitational field' in Einstein's theory, and some new material concerning the 'twin paradox' in the theory of relativity.Finally, the book contains a new section about gravitational waves, exploring the dramatic progress in this field following the LIGO observations.Based on a long-established masters course, the book serves advanced undergraduate and graduate level students, and also provides a useful reference for researchers. This book collects lectures on the general theory of relativity given by Dr. Oyvind Gron at the University of Oslo, Norway. This accessible text allows students to follow the deductions all the way throughout the book. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.
Idioma: Inglés
Editorial: Springer Nature Switzerland AG, CH, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: Rarewaves USA, OSWEGO, IL, Estados Unidos de AmericaRarewaves USA
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 57,96
Gastos de envío gratisSe envía dentro de Estados Unidos de AmericaCantidad disponible: 2 disponibles
Paperback. Condición: New. Second Edition 2020. The revised and updated 2nd edition of this established textbook provides a self-contained introduction to the general theory of relativity, describing not only the physical principles and applications of the theory, but also the mathematics needed, in particular the calculus of di…fferential forms.Updated throughout, the book contains more detailed explanations and extended discussions of several conceptual points, and strengthened mathematical deductions where required. It includes examples of work conducted in the ten years since the first edition of the book was published, for example the pedagogically helpful concept of a "river of space" and a more detailed discussion of how far the principle of relativity is contained in the general theory of relativity. Also presented is a discussion of the concept of the 'gravitational field' in Einstein's theory, and some new material concerning the 'twin paradox' in the theory of relativity.Finally, the book contains a new section about gravitational waves, exploring the dramatic progress in this field following the LIGO observations.Based on a long-established masters course, the book serves advanced undergraduate and graduate level students, and also provides a useful reference for researchers.
Idioma: Inglés
Editorial: Springer, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: GreatBookPricesUK, Woodford Green, Reino UnidoGreatBookPricesUK
Contactar con el vendedorVendedor de 5 estrellasCondición: Usado - Como Nuevo
EUR 43,64
Envío por EUR 17,51Se envía de Reino Unido a Estados Unidos de AmericaCantidad disponible: Más de 20 disponibles
Condición: As New. Unread book in perfect condition.
Idioma: Inglés
Editorial: Springer 2020-05-28, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: Chiron Media, Wallingford, Reino UnidoChiron Media
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 43,62
Envío por EUR 18,08Se envía de Reino Unido a Estados Unidos de AmericaCantidad disponible: 3 disponibles
Paperback. Condición: New.
Idioma: Inglés
Editorial: Springer, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: Basi6 International, Irving, TX, Estados Unidos de AmericaBasi6 International
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 66,76
Gastos de envío gratisSe envía dentro de Estados Unidos de AmericaCantidad disponible: 2 disponibles
Condición: Brand New. New. US edition. Expediting shipping for all USA and Europe orders excluding PO Box. Excellent Customer Service.
Idioma: Inglés
Editorial: Springer, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: Romtrade Corp., STERLING HEIGHTS, MI, Estados Unidos de AmericaRomtrade Corp.
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 69,86
Gastos de envío gratisSe envía dentro de Estados Unidos de AmericaCantidad disponible: 5 disponibles
Condición: New. This is a Brand-new US Edition. This Item may be shipped from US or any other country as we have multiple locations worldwide.
Idioma: Inglés
Editorial: Springer, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: Basi6 International, Irving, TX, Estados Unidos de AmericaBasi6 International
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 70,42
Gastos de envío gratisSe envía dentro de Estados Unidos de AmericaCantidad disponible: 8 disponibles
Condición: Brand New. New. US edition. Expediting shipping for all USA and Europe orders excluding PO Box. Excellent Customer Service.
Idioma: Inglés
Editorial: Springer, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: Books Puddle, New York, NY, Estados Unidos de AmericaBooks Puddle
Contactar con el vendedorVendedor de 4 estrellasCondición: Nuevo
EUR 67,02
Envío por EUR 3,49Se envía dentro de Estados Unidos de AmericaCantidad disponible: 3 disponibles
Condición: New.
Idioma: Inglés
Editorial: Springer, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: Biblios, frankfurt am main, HESSE, AlemaniaBiblios
Contactar con el vendedorVendedor de 4 estrellasCondición: Nuevo
EUR 60,57
Envío por EUR 9,95Se envía de Alemania a Estados Unidos de AmericaCantidad disponible: 3 disponibles
Condición: New.
Idioma: Inglés
Editorial: Springer, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: SMASS Sellers, IRVING, TX, Estados Unidos de AmericaSMASS Sellers
Contactar con el vendedorVendedor de 4 estrellasCondición: Nuevo
EUR 73,78
Gastos de envío gratisSe envía dentro de Estados Unidos de AmericaCantidad disponible: 5 disponibles
Condición: New. Brand New Original US Edition. Customer service! Satisfaction Guaranteed.
Idioma: Inglés
Editorial: Springer, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: California Books, Miami, FL, Estados Unidos de AmericaCalifornia Books
Contactar con el vendedorVendedor de 4 estrellasCondición: Nuevo
EUR 87,35
Gastos de envío gratisSe envía dentro de Estados Unidos de AmericaCantidad disponible: Más de 20 disponibles
Condición: New.
Idioma: Inglés
Editorial: Springer International Publishing, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: moluna, Greven, Alemaniamoluna
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 49,32
Envío por EUR 48,99Se envía de Alemania a Estados Unidos de AmericaCantidad disponible: 3 disponibles
Condición: New. A compact yet complete introduction to general relativity, revised to bring the content up-to-dateBased on an established lecture course the ideal student book An understandable text that is also suited for self study Incl.
Idioma: Inglés
Editorial: Springer, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: Speedyhen, Hertfordshire, Reino UnidoSpeedyhen
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 53,48
Envío por EUR 47,87Se envía de Reino Unido a Estados Unidos de AmericaCantidad disponible: 3 disponibles
Condición: NEW.
Idioma: Inglés
Editorial: Springer Nature Switzerland AG, CH, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: Rarewaves USA United, OSWEGO, IL, Estados Unidos de AmericaRarewaves USA United
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 59,74
Envío por EUR 43,72Se envía dentro de Estados Unidos de AmericaCantidad disponible: 2 disponibles
Paperback. Condición: New. Second Edition 2020. The revised and updated 2nd edition of this established textbook provides a self-contained introduction to the general theory of relativity, describing not only the physical principles and applications of the theory, but also the mathematics needed, in particular the calculus of di…fferential forms.Updated throughout, the book contains more detailed explanations and extended discussions of several conceptual points, and strengthened mathematical deductions where required. It includes examples of work conducted in the ten years since the first edition of the book was published, for example the pedagogically helpful concept of a "river of space" and a more detailed discussion of how far the principle of relativity is contained in the general theory of relativity. Also presented is a discussion of the concept of the 'gravitational field' in Einstein's theory, and some new material concerning the 'twin paradox' in the theory of relativity.Finally, the book contains a new section about gravitational waves, exploring the dramatic progress in this field following the LIGO observations.Based on a long-established masters course, the book serves advanced undergraduate and graduate level students, and also provides a useful reference for researchers.
Idioma: Inglés
Editorial: Springer Nature Switzerland AG, CH, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: Rarewaves.com UK, London, Reino UnidoRarewaves.com UK
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 44,32
Envío por EUR 75,89Se envía de Reino Unido a Estados Unidos de AmericaCantidad disponible: Más de 20 disponibles
Paperback. Condición: New. Second Edition 2020. The revised and updated 2nd edition of this established textbook provides a self-contained introduction to the general theory of relativity, describing not only the physical principles and applications of the theory, but also the mathematics needed, in particular the calculus of di…fferential forms.Updated throughout, the book contains more detailed explanations and extended discussions of several conceptual points, and strengthened mathematical deductions where required. It includes examples of work conducted in the ten years since the first edition of the book was published, for example the pedagogically helpful concept of a "river of space" and a more detailed discussion of how far the principle of relativity is contained in the general theory of relativity. Also presented is a discussion of the concept of the 'gravitational field' in Einstein's theory, and some new material concerning the 'twin paradox' in the theory of relativity.Finally, the book contains a new section about gravitational waves, exploring the dramatic progress in this field following the LIGO observations.Based on a long-established masters course, the book serves advanced undergraduate and graduate level students, and also provides a useful reference for researchers.
Idioma: Inglés
Editorial: Springer Nature Switzerland AG, Cham, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: AussieBookSeller, Truganina, VIC, AustraliaAussieBookSeller
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 87,40
Envío por EUR 32,35Se envía de Australia a Estados Unidos de AmericaCantidad disponible: 1 disponibles
Paperback. Condición: new. Paperback. The revised and updated 2nd edition of this established textbook provides a self-contained introduction to the general theory of relativity, describing not only the physical principles and applications of the theory, but also the mathematics needed, in particular the calculus of differential… forms.Updated throughout, the book contains more detailed explanations and extended discussions of several conceptual points, and strengthened mathematical deductions where required. It includes examples of work conducted in the ten years since the first edition of the book was published, for example the pedagogically helpful concept of a "river of space" and a more detailed discussion of how far the principle of relativity is contained in the general theory of relativity. Also presented is a discussion of the concept of the 'gravitational field' in Einstein's theory, and some new material concerning the 'twin paradox' in the theory of relativity.Finally, the book contains a new section about gravitational waves, exploring the dramatic progress in this field following the LIGO observations.Based on a long-established masters course, the book serves advanced undergraduate and graduate level students, and also provides a useful reference for researchers. This book collects lectures on the general theory of relativity given by Dr. Oyvind Gron at the University of Oslo, Norway. This accessible text allows students to follow the deductions all the way throughout the book. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.
Idioma: Inglés
Editorial: SPRINGER NP, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
- Edición internacional
Librería: UK BOOKS STORE, London, LONDO, Reino UnidoUK BOOKS STORE
Contactar con el vendedorVendedor de 5 estrellasEdición internacionalCondición: Nuevo
EUR 128,01
Gastos de envío gratisSe envía de Reino Unido a Estados Unidos de AmericaCantidad disponible: 1 disponibles
Condición: New. Brand New! Fast Delivery This is an International Edition and ship within 24-48 hours. Deliver by FedEx and Dhl, & Aramex, UPS, & USPS and we do accept APO and PO BOX Addresses. Order can be delivered worldwide within 6-10 days and we do have flat rate for up to 2LB. Extra shipping charges will be requested if th…e Book weight is more than 5 LB. This Item May be shipped from India, United states & United Kingdom. Depending on your location and availability.
Idioma: Inglés
Editorial: Springer Nature, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: Revaluation Books, Exeter, Reino UnidoRevaluation Books
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 117,60
Envío por EUR 14,59Se envía de Reino Unido a Estados Unidos de AmericaCantidad disponible: 2 disponibles
Paperback. Condición: Brand New. 2nd edition. 546 pages. 9.25x6.10x1.30 inches. In Stock.
Más imágenesIdioma: Inglés
Editorial: Springer, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: preigu, Osnabrück, Alemaniapreigu
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 68,35
Envío por EUR 70,00Se envía de Alemania a Estados Unidos de AmericaCantidad disponible: 5 disponibles
Taschenbuch. Condición: Neu. Introduction to Einstein's Theory of Relativity | From Newton's Attractive Gravity to the Repulsive Gravity of Vacuum Energy | Øyvind Grøn | Taschenbuch | Undergraduate Texts in Physics | xxiv | Englisch | 2020 | Springer | EAN 9783030438616 | Verantwortliche Person für die EU: Springer Verlag GmbH,…Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.
Idioma: Inglés
Editorial: Springer, 2020
Serie: Undergraduate Texts in Physics, Libro 4 de 5. Libro 4 de 5 - Undergraduate Texts in Physics
- Tapa blanda
Librería: AHA-BUCH GmbH, Einbeck, AlemaniaAHA-BUCH GmbH
Contactar con el vendedorVendedor de 5 estrellasCondición: Nuevo
EUR 81,20
Envío por EUR 64,07Se envía de Alemania a Estados Unidos de AmericaCantidad disponible: 4 disponibles
Taschenbuch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - The revised and updated 2nd edition of this established textbook provides a self-contained introduction to the general theory of relativity, describing not only the physical principles and applications of the theory, but also the mathematics needed…, in particular the calculus of differential forms.Updated throughout, the book contains more detailed explanations and extended discussions of several conceptual points, and strengthened mathematical deductions where required. It includes examples of work conducted in the ten years since the first edition of the book was published, for example the pedagogically helpful concept of a 'river of space' and a more detailed discussion of how far the principle of relativity is contained in the general theory of relativity. Also presented is a discussion of the concept of the 'gravitational field' in Einstein's theory, and some new material concerning the 'twin paradox' in the theory of relativity.Finally, the book contains a new section about gravitational waves, exploring the dramatic progress in this field following the LIGO observations.Based on a long-established masters course, the book serves advanced undergraduate and graduate level students, and also provides a useful reference for researchers.
