|
|
| Line 1: |
Line 1: |
| {{For|Sir Arthur Cayley, Baronet|Cayley baronets}}
| | BSOD or the Blue Screen of Death, (sometimes known as blue screen bodily memory dump), is an error that happens on a Windows system - when the computer merely shuts down or automatically reboots. This error could occur simply because your computer is booting up or some Windows application is running. Whenever the Windows OS discovers an unrecoverable error it hangs the system or leads to memory dumps.<br><br>However registry is conveniently corrupted and damaged when you are using the computer. Overtime, without proper maintenance, it will be loaded with errors plus incorrect or even missing info which usually make a system unable to function correctly or apply a certain task. And whenever a program may not discover the correct information, it will likely not recognize what to do. Then it freezes up! That is the real cause of the trouble.<br><br>Registry cleaning is important considering the registry may get crowded and messy whenever it happens to be left unchecked. False entries send the operating system trying to find files and directories which have lengthy ago been deleted. This takes time plus uses precious resources. So, a slowdown inevitably happens. It is particularly noticeable when you multitask.<br><br>If you feel you don't have enough cash at the time to upgrade, then the greatest choice is to free up several room by deleting a few of the unwelcome files plus folders.<br><br>If you are searching for the best [http://bestregistrycleanerfix.com/tune-up-utilities tuneup utilities 2014] system, make sure to look for one that defragments the registry. It should also scan for assorted things, such as invalid paths plus invalid shortcuts and programs. It must also identify invalid fonts, check for device driver problems and repair files. Also, make sure which it has a scheduler. That way, you are able to set it to scan the system at certain occasions on certain days. It sounds like a lot, nevertheless it is very completely vital.<br><br>Windows relies heavily on this database, storing everything from a latest emails to a Internet favorites inside there. Because it's thus important, the computer is consistently adding and updating the files inside it. This really is fine, but it will make a computer run slow, when a computer accidentally breaks its important registry files. This really is a very usual problem, plus really makes your computer run slower every day. What occurs is that because your computer is consistently using 100's of registry files at once, it occasionally gets confused and create certain of them unreadable. This then makes the computer run slow, considering Windows takes longer to read the files it demands.<br><br>Reboot PC - Just reboot a PC to find if the error is gone. Frequently, rebooting the PC readjusts the internal settings plus software and hence fixes the issue. If it doesn't then move on to follow the instructions under.<br><br>All of these difficulties may be easily solved by the clean registry. Installing our registry cleaner might allow you to utilize your PC without worries behind. You can able to employ we system without being scared which it's going to crash inside the middle. Our registry cleaner will fix a host of mistakes on a PC, identifying missing, invalid or corrupt settings in your registry. |
| {{Infobox scientist
| |
| |name = Arthur Cayley
| |
| |image = Arthur Cayley.jpg
| |
| |image_size = 240px
| |
| |caption = Portrait in London by<br />Barraud & Jerrard
| |
| |birth_date = {{birth date|1821|8|16|df=y}}
| |
| |birth_place = [[Richmond, London|Richmond]], [[Surrey]], [[UK]]
| |
| |residence = [[England]]
| |
| |nationality = [[United Kingdom|British]]
| |
| |death_date = {{death date and age|1895|1|26|1821|8|16|df=y}}
| |
| |death_place = [[Cambridge]], [[England]]
| |
| |field = [[Mathematics]]
| |
| |work_institution = [[University of Cambridge]]
| |
| |alma_mater = [[King's College School]]<br />[[Trinity College, Cambridge]]
| |
| |academic_advisors = [[George Peacock]]<br />[[William Hopkins]]
| |
| |doctoral_students = [[H. F. Baker]]<br />[[Andrew Forsyth]]<br />[[Charlotte Scott]]
| |
| |known_for = [[Projective geometry]]<br /> [[Group theory]]<br /> [[Cayley–Hamilton theorem]]
| |
| |awards = [[Copley Medal]] (1882)
| |
| |footnotes =
| |
| }}
| |
| | |
| '''Arthur Cayley''' [[Fellow_of_the_Royal_Society#Fellows|F.R.S.]] ({{IPAc-en|ˈ|k|eɪ|l|i}}; 16 August 1821 – 26 January 1895) was a [[United Kingdom|British]] [[mathematician]]. He helped found the modern British school of [[pure mathematics]].
| |
| | |
| As a child, Cayley enjoyed solving complex maths problems for amusement. He entered [[Trinity College, Cambridge]], where he excelled in [[Greek language|Greek]], [[French language|French]], [[German language|German]], and [[Italian language|Italian]], as well as [[mathematics]]. He worked as a [[lawyer]] for 14 years.
| |
| | |
| He postulated the [[Cayley–Hamilton theorem]]—that every [[square matrix]] is a root of its own [[characteristic polynomial]], and verified it for matrices of order 2 and 3.<ref>See Cayley (1858) "A Memoir on the Theory of Matrices", ''Philosophical Transactions of the Royal Society of London'', '''148''' : 24 : "I have verified the theorem, in the next simplest case, of a matrix of the order 3, … but I have not thought it necessary to undertake the labour of a formal proof of the theorem in the general case of a matrix of any degree."</ref> He was the first to define the concept of a [[group (mathematics)|group]] in the modern way—as a set with a [[Binary function|binary]] operation satisfying certain laws.<ref>Cayley (1854) [http://books.google.com/books?id=_LYConosISUC&pg=PA40#v=onepage&q&f=false "On the theory of groups, as depending on the symbolic equation θ<sup>n</sup> = 1,"] ''Philosophical Magazine'', 4th series, '''7''' (42) : 40–47. However, see also the criticism of this definition in: [http://www-history.mcs.st-and.ac.uk/HistTopics/Abstract_groups.html MacTutor: The abstract group concept].</ref> Formerly, when mathematicians spoke of "groups", they had meant [[permutation group]]s.
| |
| | |
| See also [[Cayley's theorem]].
| |
| | |
| ==Early years==
| |
| Arthur Cayley was born in [[Richmond, London]], [[England]], on 16 August 1821. His father, [[Henry Cayley]], was a distant cousin of [[George Cayley|Sir George Cayley]] the [[aeronautics]] engineer innovator, and descended from an ancient [[Yorkshire]] family. He settled in [[Saint Petersburg]], [[Russia]], as a [[merchant]]. His [[mother]] was Maria Antonia Doughty, daughter of William Doughty. According to some writers she was Russian, but her father's name indicates an English origin. His brother was the linguist [[Charles Bagot Cayley]]. Arthur spent his first eight years in Saint Petersburg. In 1829 his parents were settled permanently at [[Blackheath, London|Blackheath]], near London. Arthur was sent to a private school. He early showed great liking for, and aptitude in, numerical calculation. At age 14 he was sent to [[King's College School]]. The school's master observed indications of mathematical genius and advised the father to educate his son not for his own business, as he had intended, but to enter the [[University of Cambridge]].
| |
| | |
| ==Education==
| |
| At the unusually early age of 17 Cayley began residence at [[Trinity College, Cambridge]]. The cause of the [[Analytical Society]] had now triumphed, and the ''Cambridge Mathematical Journal'' had been instituted by Gregory and [[Robert Leslie Ellis]]. To this journal, at the age of twenty, Cayley contributed three papers, on subjects which had been suggested by reading the ''Mécanique analytique'' of [[Joseph Louis Lagrange|Lagrange]] and some of the works of [[Laplace]].
| |
| | |
| Cayley's tutor at Cambridge was [[George Peacock]] and his private coach was [[William Hopkins]]. He finished his undergraduate course by winning the place of [[Senior Wrangler]], and the first [[Smith's prize]].<ref>{{acad|id=CLY838A|name=Cayley, Arthur}}</ref> His next step was to take the M.A. degree, and win a Fellowship by competitive examination. He continued to reside at Cambridge University for four years; during which time he took some pupils, but his main work was the preparation of 28 memoirs to the '' Mathematical Journal''.
| |
| | |
| ==As a lawyer==
| |
| Because of the limited tenure of his fellowship it was necessary to choose a profession; like [[Augustus De Morgan|De Morgan]], Cayley chose law, and at age 25 entered at [[Lincoln's Inn, London]]. He made a specialty of [[conveyancing]]. It was while he was a pupil at the [[bar examination]] that he went to [[Dublin]] to hear [[William Rowan Hamilton|Hamilton]]'s lectures on [[quaternion]]s.
| |
| | |
| His friend [[James Joseph Sylvester|Sylvester]], his senior by five years at Cambridge, was then an [[actuary]], resident in London; they used to walk together round the courts of [[Lincoln's Inn]], discussing the [[theory of invariants]] and covariants. During this period of his life, extending over fourteen years, Cayley produced between two and three hundred papers.
| |
| | |
| ==As a professor==
| |
| At Cambridge University the ancient professorship of pure mathematics is denominated by the [[Lucasian Professor of Mathematics|Lucasian]], and is the chair which had been occupied by [[Isaac Newton]]. Around 1860, certain funds bequeathed by Lady Sadleir to the University, having become useless for their original purpose, were employed to establish another professorship of pure mathematics, called the [[Sadleirian Professor of Pure Mathematics|Sadleirian]]. The duties of the new professor were defined to be ''"to explain and teach the principles of pure mathematics and to apply himself to the advancement of that science."'' To this chair Cayley was elected when 42 years old. He gave up a lucrative practice for a modest salary; but he never regretted the exchange, for the chair at Cambridge enabled him to end the divided allegiance between law and mathematics, and to devote his energies to the pursuit which he liked best. He at once married and settled down in Cambridge. More fortunate than Hamilton in his choice, his home life was one of great happiness. His friend and fellow investigator, Sylvester, once remarked that Cayley had been much more fortunate than himself; that they both lived as bachelors in London, but that Cayley had married and settled down to a quiet and peaceful life at Cambridge; whereas he had never married, and had been fighting the world all his days.
| |
| | |
| At first the teaching duty of the Sadleirian professorship was limited to a course of lectures extending over one of the terms of the academic year; but when the University was reformed about 1886, and part of the college funds applied to the better endowment of the University professors, the lectures were extended over two terms. For many years the attendance was small, and came almost entirely from those who had finished their career of preparation for competitive examinations; after the reform the attendance numbered about fifteen. The subject lectured on was generally that of the memoir on which the professor was for the time engaged.
| |
| | |
| The other duty of the chair — the advancement of mathematical science — was discharged in a handsome manner by the long series of memoirs which he published, ranging over every department of pure mathematics. But it was also discharged in a much less obtrusive way; he became the standing referee on the merits of mathematical papers to many societies both at home and abroad.
| |
| | |
| In 1876 he published a ''Treatise on [[elliptic function|Elliptic Functions]]'', which was his only book. He took great interest in the movement for the University education of women. At Cambridge the women's colleges are Girton and Newnham. In the early days of [[Girton College]] he gave direct help in teaching, and for some years he was chairman of the council of [[Newnham College]], in the progress of which he took the keenest interest to the last.
| |
| | |
| In 1872 he was made an honorary fellow of Trinity College, and three years later an ordinary fellow, which meant stipend as well as honour. About this time his friends subscribed for a presentation portrait. [[James Clerk Maxwell|Maxwell]] wrote an address to the committee of subscribers who had charge of the Cayley portrait fund. The verses refer to the subjects investigated in several of Cayley's most elaborate memoirs; such as, Chapters on the Analytical Geometry of <math>n</math> dimensions; On the theory of [[Determinant]]s; Memoir on the theory of Matrices; Memoirs on skew surfaces, otherwise Scrolls; On the delineation of a Cubic Scroll, etc.<ref>[[s:To the Committee of the Cayley Portrait Fund|"To the Committee of the Cayley Portrait Fund"]], 1874</ref>
| |
| | |
| In 1881 he received from the [[Johns Hopkins University]], Baltimore, where Sylvester was then professor of mathematics, an invitation
| |
| to deliver a course of lectures. He accepted the invitation, and lectured at Baltimore during the first five months of 1882 on the | |
| subject of the ''Abelian and Theta Functions''.
| |
| | |
| ==BMA==
| |
| | |
| In 1883 Cayley was President of the [[British Association for the Advancement of Science]]. The meeting was held at Southport, in the north of England. As the President's address is one of the great popular events of the meeting, and brings out an audience of general culture, it is usually made as little technical as possible. {{harvtxt|Cayley|1996}} took for his subject the Progress of Pure Mathematics.
| |
| | |
| He is buried in the [[Mill Road Cemetery, Cambridge|Mill Road cemetery]], Cambridge.
| |
| | |
| ==The ''Collected Papers''==
| |
| In 1889 the [[Cambridge University Press]] requested him to prepare his mathematical papers for publication in a collected form—a request which he appreciated very much. They are printed in magnificent [[Bookbinding|quarto volume]]s, of which seven appeared under his own editorship. While editing these volumes, he was suffering from a painful internal malady, to which he succumbed on 26 January 1895, in the 74th year of his age. When the funeral took place, a great assemblage met in Trinity Chapel, comprising members of the University, official representatives of Russia and America, and many of the most illustrious philosophers of [[United Kingdom|Britain]].
| |
| | |
| The remainder of his papers were edited by [[Andrew Forsyth]], his successor in the Sadleirian Chair. The Collected Mathematical papers number thirteen quarto volumes, and contain 967 papers. Cayley retained to the last his fondness for novel-reading and for travelling. He also took special pleasure in paintings and architecture, and he practiced [[Watercolor painting|water-color painting]], which he found useful sometimes in making mathematical diagrams.
| |
| | |
| ==Legacy==
| |
| <div style="-moz-column-count:4; column-count:4;"> | |
| * [[Cayley's theorem]]
| |
| * [[Cayley–Hamilton theorem]] in [[linear algebra]]
| |
| * [[Grassmann–Cayley algebra]]
| |
| * [[Cayley–Menger determinant]]
| |
| * [[Cayley diagram]]s – used for finding [[cognate linkage]]s in mechanical engineering
| |
| * [[Cayley–Dickson construction]]
| |
| * [[Octonion|Cayley algebra]]
| |
| * [[Cayley graph]]
| |
| * [[Cayley numbers]]
| |
| * [[Cayley table]]
| |
| * [[Cayley–Purser algorithm]]
| |
| * [[Cayley's formula]]
| |
| * [[Cayley–Klein metric]]
| |
| * [[Klein model|Cayley–Klein model]] of [[hyperbolic geometry]]
| |
| * [[Cayley's Ω process]]
| |
| * [[Cayley surface (disambiguation)|Cayley surface]]
| |
| * [[Cayley transform]]
| |
| * [[Cayley's nodal cubic surface]]
| |
| * [[Cayley's ruled cubic surface]]
| |
| * The crater [[Cayley (crater)|Cayley]] on the [[Moon]] (and consequently the Cayley Formation, a geological unit named after the crater)
| |
| * [[Cayley's mousetrap]] — a card game
| |
| * [[Cayleyan]]
| |
| * [[Chasles–Cayley–Brill formula]]
| |
| * [[Quippian]]
| |
| </div> | |
| | |
| ==Bibliography==
| |
| *{{Citation | last1=Cayley | first1=Arthur | author1-link=Arthur Cayley | title=An elementary treatise on elliptic functions | origyear=1876 | url=http://www.archive.org/details/anelementarytre01caylgoog | publisher=Cornell University Library | isbn=978-1-112-28006-1 | mr=0124532 | year=2009}}
| |
| *{{Citation | last1=Cayley | first1=Arthur | author1-link=Arthur Cayley | title=The Collected Mathematical Papers | origyear=1889 | url=http://quod.lib.umich.edu/cgi/t/text/text-idx?c=umhistmath;idno=ABS3153 | publisher=[[Cambridge University Press]] | series=Cambridge Library Collection – Mathematics | isbn=978-1-108-00507-4 | id=[http://www.archive.org/search.php?query=The_collected_mathematical_papers_of_Arthur_Cayley archive] | year=2009 | volume=14 volumes}}
| |
| | |
| == See also ==
| |
| | |
| * [[List of things named after Arthur Cayley]]
| |
| | |
| ==References==
| |
| <references />
| |
| *{{Citation | last1=Cayley | first1=Arthur | author1-link=Arthur Cayley | editor1-last=Ewald | editor1-first=William | title=From Kant to Hilbert: a source book in the foundations of mathematics. Vol. I, II | origyear=1883 | url=http://books.google.com/books?id=Yil-EmrsT2wC | publisher=The Clarendon Press [[Oxford University Press]] | series=Oxford Science Publications | isbn=978-0-19-853271-2 | mr=1465678 |id=[http://www.archive.org/stream/collmathpapers11caylrich#page/n451/mode/2up Reprinted in collected matheamtical papers volume 11] | year=1996 | chapter=Presidential address to the British Association | pages=542–573}}
| |
| *{{Citation | last1=Crilly | first1=Tony | title=A Victorian Mathematician: Arthur Cayley (1821–1895) | jstor=3618297 | publisher=[[The Mathematical Association]] | year=1995 | journal=[[The Mathematical Gazette]] | issn=0025-5572 | volume=79 | issue=485 | pages=259–262 | doi=10.2307/3618297}}
| |
| *{{Citation | last1=Crilly | first1=Tony | title=Arthur Cayley. Mathematician laureate of the Victorian age | url=http://books.google.com/books?isbn=0801880114 | publisher=[[Johns Hopkins University Press]] | isbn=978-0-8018-8011-7 | mr=2284396 | year=2006}}
| |
| *{{Citation | last1=Macfarlane | first1=Alexander | authorlink=Alexander Macfarlane| title=Lectures on Ten British Mathematicians of the Nineteenth Century | origyear=1916 | url=http://www.archive.org/details/lecturesontenbri00macf | publisher=[[Cornell University Library]] | series=Mathematical monographs | isbn=978-1-112-28306-2 | year=2009 | volume=17}} ([http://library.beau.org/gutenberg/etext06/tbmms10p.pdf complete text] at [[Project Gutenberg]])
| |
| | |
| ==External links==
| |
| {{wikisource author}}
| |
| * {{MacTutor Biography|id=Cayley}}
| |
| * {{MathGenealogy|id=7824}}
| |
| * {{ScienceWorldBiography | urlname=Cayley | title=Cayley, Arthur (1821–1895)}}
| |
| | |
| {{Copley Medallists 1851-1900}}
| |
| | |
| {{Authority control|VIAF=69046313}}
| |
| {{Persondata<!--Metadata: see [[Wikipedia:Persondata]]-->
| |
| |NAME= Cayley, Arthur
| |
| |ALTERNATIVE NAMES=
| |
| |SHORT DESCRIPTION= [[UK|British]] [[mathematician]]
| |
| |DATE OF BIRTH= August 16, 1821
| |
| |PLACE OF BIRTH= [[Richmond, London|Richmond]], [[Surrey]], [[UK]]
| |
| |DATE OF DEATH= January 26, 1895
| |
| |PLACE OF DEATH= [[Cambridge]], [[UK]]
| |
| }}
| |
| {{DEFAULTSORT:Cayley, Arthur}}
| |
| [[Category:1821 births]]
| |
| [[Category:1895 deaths]]
| |
| [[Category:19th-century British mathematicians]]
| |
| [[Category:Group theorists]]
| |
| [[Category:Algebraic geometers]]
| |
| [[Category:Graph theorists]]
| |
| [[Category:People educated at King's College School, Wimbledon]]
| |
| [[Category:Newnham College, Cambridge]]
| |
| [[Category:Alumni of Trinity College, Cambridge]]
| |
| [[Category:Academics of the University of Cambridge]]
| |
| [[Category:Fellows of Trinity College, Cambridge]]
| |
| [[Category:Magic squares]]
| |
| [[Category:Recipients of the Copley Medal]]
| |
| [[Category:Royal Medal winners]]
| |
| [[Category:Senior Wranglers]]
| |
| [[Category:Fellows of the Royal Society]]
| |
| [[Category:Presidents of the British Science Association]]
| |
| [[Category:De Morgan Medallists]]
| |
| [[Category:Burials in Cambridge]]
| |
BSOD or the Blue Screen of Death, (sometimes known as blue screen bodily memory dump), is an error that happens on a Windows system - when the computer merely shuts down or automatically reboots. This error could occur simply because your computer is booting up or some Windows application is running. Whenever the Windows OS discovers an unrecoverable error it hangs the system or leads to memory dumps.
However registry is conveniently corrupted and damaged when you are using the computer. Overtime, without proper maintenance, it will be loaded with errors plus incorrect or even missing info which usually make a system unable to function correctly or apply a certain task. And whenever a program may not discover the correct information, it will likely not recognize what to do. Then it freezes up! That is the real cause of the trouble.
Registry cleaning is important considering the registry may get crowded and messy whenever it happens to be left unchecked. False entries send the operating system trying to find files and directories which have lengthy ago been deleted. This takes time plus uses precious resources. So, a slowdown inevitably happens. It is particularly noticeable when you multitask.
If you feel you don't have enough cash at the time to upgrade, then the greatest choice is to free up several room by deleting a few of the unwelcome files plus folders.
If you are searching for the best tuneup utilities 2014 system, make sure to look for one that defragments the registry. It should also scan for assorted things, such as invalid paths plus invalid shortcuts and programs. It must also identify invalid fonts, check for device driver problems and repair files. Also, make sure which it has a scheduler. That way, you are able to set it to scan the system at certain occasions on certain days. It sounds like a lot, nevertheless it is very completely vital.
Windows relies heavily on this database, storing everything from a latest emails to a Internet favorites inside there. Because it's thus important, the computer is consistently adding and updating the files inside it. This really is fine, but it will make a computer run slow, when a computer accidentally breaks its important registry files. This really is a very usual problem, plus really makes your computer run slower every day. What occurs is that because your computer is consistently using 100's of registry files at once, it occasionally gets confused and create certain of them unreadable. This then makes the computer run slow, considering Windows takes longer to read the files it demands.
Reboot PC - Just reboot a PC to find if the error is gone. Frequently, rebooting the PC readjusts the internal settings plus software and hence fixes the issue. If it doesn't then move on to follow the instructions under.
All of these difficulties may be easily solved by the clean registry. Installing our registry cleaner might allow you to utilize your PC without worries behind. You can able to employ we system without being scared which it's going to crash inside the middle. Our registry cleaner will fix a host of mistakes on a PC, identifying missing, invalid or corrupt settings in your registry.