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George Boole

George Boole was a self-taught English mathematician and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Ireland. He worked in the fields of differential equations and algebraic logic, is best known as the author of The Laws of Thought which contains Boolean algebra. Boolean logic is credited with laying the foundations for the information age. Boole maintained that: No general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognise, not only the special numerical bases of the science, but those universal laws of thought which are the basis of all reasoning, which, whatever they may be as to their essence, are at least mathematical as to their form. Boole was born in Lincoln, England, the son of John Boole senior, a shoemaker and Mary Ann Joyce, he had a primary school education, received lessons from his father, but due to a serious decline in business, he had little further formal and academic teaching.

William Brooke, a bookseller in Lincoln, may have helped him with Latin, which he may have learned at the school of Thomas Bainbridge. He was self-taught in modern languages. In fact, when a local newspaper printed his translation of a Latin poem, a scholar accused him of plagiarism under the pretence that he was not capable of such achievements. At age 16, Boole became the breadwinner for his parents and three younger siblings, taking up a junior teaching position in Doncaster at Heigham's School, he taught in Liverpool. Boole participated in the Mechanics Institute, in the Greyfriars, founded in 1833. Edward Bromhead, who knew John Boole through the institution, helped George Boole with mathematics books and he was given the calculus text of Sylvestre François Lacroix by the Rev. George Stevens Dickson of St Swithin's, Lincoln. Without a teacher, it took him many years to master calculus. At age 19, Boole established his own school in Lincoln, he continued making his living by running schools.

Four years he took over Hall's Academy in Waddington, outside Lincoln, following the death of Robert Hall. In 1840 he moved back to Lincoln. Boole became involved in the Lincoln Topographical Society, serving as a member of the committee, presenting a paper entitled, On the origin and tendencies of Polytheism amongst the ancient Egyptians and Persians, in modern India. On 30 November 1841. Boole became a prominent local figure, an admirer of John Kaye, the bishop, he took part in the local campaign for early closing. With Edmund Larken and others he set up a building society in 1847, he associated with the Chartist Thomas Cooper, whose wife was a relation. From 1838 onwards Boole was making contacts with sympathetic British academic mathematicians and reading more widely, he studied algebra in the form of symbolic methods, as far as these were understood at the time, began to publish research papers. After receiving positive feedback on his publications, he considered attending the University of Cambridge, but decided against attending when told he would have to start with the standard undergraduate courses and discontinue his own research.

Boole's status as mathematician was recognised by his appointment in 1849 as the first professor of mathematics at Queen's College, Cork in Ireland. He met his future wife, Mary Everest, there in 1850 while she was visiting her uncle John Ryall, professor of Greek, they married some years in 1855. He maintained his ties with Lincoln, working there with E. R. Larken in a campaign to reduce prostitution. In 1844 Boole's paper On a General Method for Analysis won the first gold prize for mathematics awarded by the Royal Society, he was awarded the Keith Medal by the Royal Society of Edinburgh in 1855 and was elected a Fellow of the Royal Society in 1857. He received honorary degrees of LL. D. from the University of Dublin and the University of Oxford. Boole's first published paper was Researches in the theory of analytical transformations, with a special application to the reduction of the general equation of the second order, printed in the Cambridge Mathematical Journal in February 1840, it led to a friendship between Boole and Duncan Farquharson Gregory, the editor of the journal.

His works are in a few separate publications. In 1841 Boole published an influential paper in early invariant theory, he received a medal from the Royal Society On A General Method of Analysis. It was a contribution to the theory of linear differential equations, moving from the case of constant coefficients on which he had published, to variable coefficients; the innovation in operational methods is to admit. In 1847 Boole published The Mathematical Analysis of Logic, the first of his works on symbolic logic. Boole completed two systematic treatises on mathematical subjects during his lifetime; the Treatise on Differential Equations appeared in 1859, was followed, the next year, by a Treatise on the Calculus of Finite Differences, a sequel to the former work. In 1857, Boole published the treatise On the Comparison of Transcendent, with Certain Applications to the Theory of Definite Integrals, in which he studied the sum of residues of a rational function. Among other results, he proved what is now called Boole's identity: m e s { x ∈ R ∣ ℜ 1 π ∑ a

Range (particle radiation)

In passing through matter, charged particles ionize and thus lose energy in many steps, until their energy is zero. The distance to this point is called the range of the particle; the range depends on the type of particle, on its initial energy and on the material through which it passes. For example, if the ionising particle passing through the material is a positive ion like an alpha particle or proton, it will collide with atomic electrons in the material via Coulombic interaction. Since the mass of the proton or alpha particle is much greater than that of the electron, there will be no significant deviation from the radiation's incident path and little kinetic energy will be lost in each collision; as such, it will take many successive collisions for such heavy ionising radiation to come to a halt within the stopping medium or material. Maximum energy loss will take place in a head-on collision with an electron. Since large angle scattering is rare for positive ions, a range may be well defined for that radiation, depending on its energy and charge, as well as the ionisation energy of the stopping medium.

Since the nature of such interactions is statistical, the number of collisions required to bring a radiation particle to rest within the medium will vary with each particle. Hence, there will be a small variation in the range, known as straggling; the energy loss per unit distance, or stopping power depends on the type and energy of the particle and on the material. The energy loss per unit distance increases while the particle slows down; the curve describing this fact is called the Bragg curve. Shortly before the end, the energy loss passes through a maximum, the Bragg Peak, drops to zero; this fact is of great practical importance for radiation therapy. The range of alpha particles in ambient air amounts to only several centimeters. Although beta particles scatter much more than alpha particles, a range can still be defined; the mean range can be calculated by integrating the inverse stopping power over energy. The range of a heavy charged particle is proportional to the mass of the particle and the inverse of the density of the medium, is a function of the initial velocity of the particle.

Stopping power Attenuation length Radiation length Nakamura, K. "Review of Particle Physics". Journal of Physics G: Nuclear and Particle Physics. 37: 075021. Bibcode:2010JPhG...37g5021N. Doi:10.1088/0954-3899/37/7A/075021. Williams, William S. C.. Nuclear and particle physics. Oxford: Clarendon Press. ISBN 978-0-19-852046-7. Leo, William R.. Techniques for nuclear and particle physics experiments: a how-to approach. Berlin: Springer. ISBN 978-3-540-57280-0

2001 Clarion Sandown 500

The 2001 Clarion Sandown 500 was an Australian motor race for Sports and Production Cars which drew its entries from those competing in the Australian Nations Cup Championship and Australian GT Production Car Championship. It was the first Sandown 500 held since the former touring car endurance race was revived for production cars; the race, the 34th Sandown 500 endurance race was held at Sandown Raceway in Melbourne, Australia over the weekend of 15 September 2001. Cars competed in four classes: Nations Cup GT Production Class A GT Production Class B GT Production Class C After qualifying was completed the fastest ten cars competed in a one-lap runoff for the top ten grid positions. Runoff results as follows: Cars failing to complete 75% of winner's distance marked as Not Classified. Race results as follows: Provisional Pole Position - #666 Paul Stokell - 1:16.4012 Pole Position - #43 Jim Richards - 1:16.9760 Fastest Lap - #7 D'arcy Russell - 1:17.7024 Race Average Speed - 143.22 km/h Images from the 2001 Clarion Sandown 500 Retrieved from web.archive.org on 19 January 2009