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Selmer M. Johnson
Selmer Martin Johnson (21 May 1916 – 26 June 1996) was an American mathematician, a researcher at the RAND Corporation. Biography Johnson was born on May 21, 1916, in Buhl, Minnesota. He earned a B.A. and then an M.A. in mathematics from the University of Minnesota in 1938 and 1940 respectively. World War II interrupted Johnson's mathematical studies: he enlisted in the United States Air Force, earning the rank of major. While serving, he also earned an M.S. in meteorology from New York University in 1942. After the war, Johnson returned to graduate study in mathematics at the University of Illinois at Urbana–Champaign, finishing his doctorate in 1950; his dissertation, on the subject of number theory, was supervised by David Bourgin, a student of George David Birkhoff.Contributors, ''IRE Transactions on Information Theory'', April 1962, p. 261. This section may be seen attached to ; Johnson's paper, "A new upper bound for error-correcting codes", appears earlier in the same i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RAND Corporation
The RAND Corporation (from the phrase "research and development") is an American nonprofit global policy think tank created in 1948 by Douglas Aircraft Company to offer research and analysis to the United States Armed Forces. It is financed by the Federal government of the United States, U.S. government and private Financial endowment, endowment, corporations, university, universities and private individuals. The company assists other governments, international organizations, private companies and foundations with a host of defense and non-defense issues, including healthcare. RAND aims for interdisciplinary and quantitative problem solving by translating theory, theoretical concepts from formal economics and the Outline of physical science, physical sciences into novel applications in other areas, using applied science and operations research. Overview RAND has approximately 1,850 employees. Its American locations include: Santa Monica, California (headquarters); Arlington ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ford–Johnson Algorithm
In computer science, merge-insertion sort or the Ford–Johnson algorithm is a comparison sorting algorithm published in 1959 by L. R. Ford Jr. and Selmer M. Johnson. It uses fewer comparisons in the worst case than the best previously known algorithms, binary insertion sort and merge sort, and for 20 years it was the sorting algorithm with the fewest known comparisons. Although not of practical significance, it remains of theoretical interest in connection with the problem of sorting with a minimum number of comparisons. The same algorithm may have also been independently discovered by Stanisław Trybuła and Czen Ping. Algorithm Merge-insertion sort performs the following steps, on an input X of n elements: #Group the elements of X into \lfloor n/2\rfloor pairs of elements, arbitrarily, leaving one element unpaired if there is an odd number of elements. #Perform \lfloor n/2\rfloor comparisons, one per pair, to determine the larger of the two elements in each pair. #Recursively ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Illinois Urbana-Champaign Alumni
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the designation is reserved for colleges that have a graduate school. The word ''university'' is derived from the Latin ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". The first universities were created in Europe by Catholic Church monks. The University of Bologna (''Università di Bologna''), founded in 1088, is the first university in the sense of: *Being a high degree-awarding institute. *Having independence from the ecclesiastic schools, although conducted by both clergy and non-clergy. *Using the word ''universitas'' (which was coined at its foundation). *Issuing secular and non-secular degrees: grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New York University Alumni
New is an adjective referring to something recently made, discovered, or created. New or NEW may refer to: Music * New, singer of K-pop group The Boyz Albums and EPs * ''New'' (album), by Paul McCartney, 2013 * ''New'' (EP), by Regurgitator, 1995 Songs * "New" (Daya song), 2017 * "New" (Paul McCartney song), 2013 * "New" (No Doubt song), 1999 *"new", by Loona from '' Yves'', 2017 *"The New", by Interpol from ''Turn On the Bright Lights'', 2002 Acronyms * Net economic welfare, a proposed macroeconomic indicator * Net explosive weight, also known as net explosive quantity * Network of enlightened Women, a conservative university women's organization * Next Entertainment World, a South Korean film distribution company Identification codes * Nepal Bhasa language ISO 639 language code * New Century Financial Corporation (NYSE stock abbreviation) * Northeast Wrestling, a professional wrestling promotion in the northeastern United States Transport * New Orleans Lakefront Ai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Minnesota College Of Liberal Arts Alumni
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the designation is reserved for colleges that have a graduate school. The word ''university'' is derived from the Latin ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". The first universities were created in Europe by Catholic Church monks. The University of Bologna (''Università di Bologna''), founded in 1088, is the first university in the sense of: *Being a high degree-awarding institute. *Having independence from the ecclesiastic schools, although conducted by both clergy and non-clergy. *Using the word ''universitas'' (which was coined at its foundation). *Issuing secular and non-secular degrees: grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1996 Deaths
File:1996 Events Collage.png, From left, clockwise: A bomb explodes at Centennial Olympic Park in Atlanta, set off by a radical anti-abortionist; The center fuel tank explodes on TWA Flight 800, causing the plane to crash and killing everyone on board; Eight people die in a blizzard on Mount Everest; Dolly the Sheep becomes the first mammal to have been cloned from an adult somatic cell; The Port Arthur Massacre occurs on Tasmania, and leads to major changes in Australia's gun laws; Macarena, sung by Los del Río and remixed by The Bayside Boys, becomes a major dance craze and cultural phenomenon; Ethiopian Airlines Flight 961 crash-ditches off of the Comoros Islands after the plane was hijacked; the 1996 Summer Olympics are held in Atlanta, marking the Centennial (100th Anniversary) of the modern Olympic Games., 300x300px, thumb rect 0 0 200 200 Centennial Olympic Park bombing rect 200 0 400 200 TWA FLight 800 rect 400 0 600 200 1996 Mount Everest disaster rect 0 200 30 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1916 Births
Events Below, the events of the First World War have the "WWI" prefix. January * January 1 – The British Empire, British Royal Army Medical Corps carries out the first successful blood transfusion, using blood that had been stored and cooled. * January 9 – WWI: Gallipoli Campaign: The last British troops are evacuated from Gallipoli, as the Ottoman Empire prevails over a joint British and French operation to capture Constantinople. * January 10 – WWI: Erzurum Offensive: Russia defeats the Ottoman Empire. * January 12 – The Gilbert and Ellice Islands Colony, part of the British Empire, is established in present-day Tuvalu and Kiribati. * January 13 – WWI: Battle of Wadi (1916), Battle of Wadi: Ottoman Empire forces defeat the British, during the Mesopotamian campaign in modern-day Iraq. * January 29 – WWI: Paris is bombed by German Empire, German zeppelins. * January 31 – WWI: An attack is planned on Verdun, France. February * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johnson Counter
A ring counter is a type of counter composed of flip-flops connected into a shift register, with the output of the last flip-flop fed to the input of the first, making a "circular" or "ring" structure. There are two types of ring counters: * A straight ring counter, also known as a one-hot counter, connects the output of the last shift register to the first shift register input and circulates a single one (or zero) bit around the ring. * A twisted ring counter, also called switch-tail ring counter, walking ring counter, Johnson counter, or Möbius counter, connects the complement of the output of the last shift register to the input of the first register and circulates a stream of ones followed by zeros around the ring. Four-bit ring-counter sequences Properties Ring counters are often used in hardware design (e.g. ASIC and FPGA design) to create finite-state machines. A binary counter would require an adder circuit which is substantially more complex than a ring count ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johnson Bound
In applied mathematics, the Johnson bound (named after Selmer Martin Johnson) is a limit on the size of error-correcting codes, as used in coding theory for data transmission or communications. Definition Let C be a ''q''-ary code of length n, i.e. a subset of \mathbb_q^n. Let d be the minimum distance of C, i.e. :d = \min_ d(x,y), where d(x,y) is the Hamming distance between x and y. Let C_q(n,d) be the set of all ''q''-ary codes with length n and minimum distance d and let C_q(n,d,w) denote the set of codes in C_q(n,d) such that every element has exactly w nonzero entries. Denote by , C, the number of elements in C. Then, we define A_q(n,d) to be the largest size of a code with length n and minimum distance d: : A_q(n,d) = \max_ , C, . Similarly, we define A_q(n,d,w) to be the largest size of a code in C_q(n,d,w): : A_q(n,d,w) = \max_ , C, . Theorem 1 (Johnson bound for A_q(n,d)): If d=2t+1, : A_q(n,d) \leq \frac. If d=2t+2, : A_q(n,d) \leq \frac. Theorem 2 (Joh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steinhaus–Johnson–Trotter Algorithm
The Steinhaus–Johnson–Trotter algorithm or Johnson–Trotter algorithm, also called plain changes, is an algorithm named after Hugo Steinhaus, Selmer M. Johnson and Hale F. Trotter that generates all of the permutations of n elements. Each permutation in the sequence that it generates differs from the previous permutation by swapping two adjacent elements of the sequence. Equivalently, this algorithm finds a Hamiltonian cycle in the permutohedron. This method was known already to 17th-century English change ringers, and calls it "perhaps the most prominent permutation enumeration algorithm". A version of the algorithm can be implemented in such a way that the average time per permutation is constant. As well as being simple and computationally efficient, this algorithm has the advantage that subsequent computations on the permutations that it generates may be sped up because of the similarity between consecutive permutations that it generates.. Algorithm The sequence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johnson Scheme
In mathematics, the Johnson scheme, named after Selmer M. Johnson, is also known as the triangular association scheme. It consists of the set of all binary vectors ''X'' of length ''ℓ'' and weight ''n'', such that v=\left, X\=\binom.F. J. MacWilliams and N. J. A. Sloane, ''The Theory of Error-Correcting Codes'', Elsevier, New York, 1978. Two vectors ''x'', ''y'' ∈ ''X'' are called ''i''th associates if dist(''x'', ''y'') = 2''i'' for ''i'' = 0, 1, ..., ''n''. The eigenvalues In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted b ... are given by : p_\left(k\right)=E_\left(k\right), : q_\left(i\right)=\fracE_\left(k\right), where : \mu_=\frac\binom, and ''E''''k''(''x'') is an Eberlein polynomial defined by : E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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