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Tutte Path
William Thomas Tutte (; 14 May 1917 – 2 May 2002) was an English and Canadian code breaker and mathematician. During the Second World War, he made a fundamental advance in cryptanalysis of the Lorenz cipher, a major Nazi German cipher system which was used for top-secret communications within the Wehrmacht High Command. The high-level, strategic nature of the intelligence obtained from Tutte's crucial breakthrough, in the bulk decrypting of Lorenz-enciphered messages specifically, contributed greatly, and perhaps even decisively, to the defeat of Nazi Germany. He also had a number of significant mathematical accomplishments, including foundation work in the fields of graph theory and matroid theory. Tutte's research in the field of graph theory proved to be of remarkable importance. At a time when graph theory was still a primitive subject, Tutte commenced the study of matroids and developed them into a theory by expanding from the work that Hassler Whitney had first develop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Newmarket, Suffolk
Newmarket is a market town and civil parish in the West Suffolk (district), West Suffolk district of Suffolk, England, 14 miles west of Bury St Edmunds and 14 miles northeast of Cambridge. In 2021, it had a population of 16,772. It is a global centre for thoroughbred horse race, thoroughbred horse racing, racehorse training, breeding, and horse health. Two Classic races and three British Champions Series races are held at Newmarket every year. The town has had close royal connections since the time of James I of England, James I, who built a palace there, and was also a base for Charles I of England, Charles I, Charles II of England, Charles II, and most monarchs since. Elizabeth II visited the town often to see her horses in training. Newmarket has over fifty horse training stables, two large racetracks, the Rowley Mile and the Newmarket Racecourse, July Course, and one of the most extensive and prestigious horse training grounds in the world. The town is home to over 3,500 rac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Tutte Polynomial
The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a graph polynomial. It is a polynomial in two variables which plays an important role in graph theory. It is defined for every undirected graph G and contains information about how the graph is connected. It is denoted by T_G. The importance of this polynomial stems from the information it contains about G. Though originally studied in algebraic graph theory as a generalization of counting problems related to graph coloring and nowhere-zero flow, it contains several famous other specializations from other sciences such as the Jones polynomial from knot theory and the partition functions of the Potts model from statistical physics. It is also the source of several central computational problems in theoretical computer science. The Tutte polynomial has several equivalent definitions. It is essentially equivalent to Whitney’s rank polynomial, Tutte’s own dichromatic polynomial and Fortuin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Cryptanalysis Of The Lorenz Cipher
Cryptanalysis of the Lorenz cipher was the process that enabled the British to read high-level German army messages during World War II. The British Government Code and Cypher School (GC&CS) at Bletchley Park decrypted many communications between the ''Oberkommando der Wehrmacht'' (OKW, German High Command) in Berlin and their army commands throughout occupied Europe, some of which were signed "Adolf Hitler, Führer". These were intercepted non-Morse code, Morse radio transmissions that had been enciphered by the Lorenz cipher, Lorenz SZ teleprinter Rotor machine, rotor stream cipher attachments. Decrypts of this traffic became an important source of "Ultra (cryptography), Ultra" intelligence, which contributed significantly to Allied victory. For its high-level secret messages, the German armed services enciphered each Character (computing), character using various online ''Geheimschreiber'' (secret writer) stream cipher machines at both ends of a Electrical telegraph, telegraph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Second World War
World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the world's countries participated, with many nations mobilising all resources in pursuit of total war. Tanks in World War II, Tanks and Air warfare of World War II, aircraft played major roles, enabling the strategic bombing of cities and delivery of the Atomic bombings of Hiroshima and Nagasaki, first and only nuclear weapons ever used in war. World War II is the List of wars by death toll, deadliest conflict in history, causing World War II casualties, the death of 70 to 85 million people, more than half of whom were civilians. Millions died in genocides, including the Holocaust, and by massacres, starvation, and disease. After the Allied victory, Allied-occupied Germany, Germany, Allied-occupied Austria, Austria, Occupation of Japan, Japan, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Cryptanalysis
Cryptanalysis (from the Greek ''kryptós'', "hidden", and ''analýein'', "to analyze") refers to the process of analyzing information systems in order to understand hidden aspects of the systems. Cryptanalysis is used to breach cryptographic security systems and gain access to the contents of encrypted messages, even if the cryptographic key is unknown. In addition to mathematical analysis of cryptographic algorithms, cryptanalysis includes the study of side-channel attacks that do not target weaknesses in the cryptographic algorithms themselves, but instead exploit weaknesses in their implementation. Even though the goal has been the same, the methods and techniques of cryptanalysis have changed drastically through the history of cryptography, adapting to increasing cryptographic complexity, ranging from the pen-and-paper methods of the past, through machines like the British Bombes and Colossus computers at Bletchley Park in World War II, to the mathematically advanced ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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CRM-Fields-PIMS Prize
The CRM-Fields-PIMS Prize is the premier Canadian research prize in the mathematical sciences. It is awarded in recognition of exceptional research achievement in the mathematical sciences and is given annually by three Canadian mathematics institutes: the Centre de Recherches Mathématiques (CRM), the Fields Institute, and the Pacific Institute for the Mathematical Sciences (PIMS). The prize was established in 1994 by the CRM and the Fields Institute as the CRM-Fields Prize. The prize took its current name when PIMS became a partner in 2005. The prize carries a monetary award of $10,000, funded jointly by the three institutes. The inaugural prize winner was H.S.M. Coxeter. Winners Source: Centre de recherches mathématiques *1995 – H. S. M. Coxeter *1996 – George A. Elliott *1997 – James Arthur *1998 – Robert V. Moody *1999 – Stephen A. Cook *2000 – Israel Michael Sigal *2001 – William T. Tutte *2002 – John B. Friedlander *2003 – John McKay and Edwin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Isaak-Walton-Killam Award
The Killam Prize (previously the Izaak Walton Killam Memorial Prize) was established according to the will of Dorothy J. Killam to honour the memory of her husband Izaak Walton Killam. Five Killam Prizes, each having a value of $100,000, were awarded annually by the Canada Council for the Arts to eminent Canadian researchers who distinguish themselves in the fields of social sciences, humanities, natural sciences, health sciences, or engineering. In August 2021, the Canada Council announced it would transition the administration of the Killam program to the National Research Council Canada (NRC) by March 2022. The restructured Killam Program was officially launched under the administration of the NRC in April 2022. It is now called the National Killam Program and consists of the Killam Prizes, the Dorothy Killam Fellowships and the Killam NRC Paul Corkum Fellowships. Recipients See also * List of medicine awards * List of social sciences awards This list of social scie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Henry Marshall Tory Medal
The Henry Marshall Tory Medal is an award of the Royal Society of Canada The Royal Society of Canada (RSC; , SRC), also known as the Academies of Arts, Humanities, and Sciences of Canada (French: ''Académies des arts, des lettres et des sciences du Canada''), is the senior national, bilingual council of distinguishe ... "for outstanding research in a branch of astronomy, chemistry, mathematics, physics, or an allied science". It is named in honour of Henry Marshall Tory and is awarded bi-annually. The award consists of a gold plated silver medal. Recipients Source Royal Society of Canada See also * List of general science and technology awards * List of awards named after people References * {{Royal Society of Canada Canadian science and technology awards Royal Society of Canada Awards established in 1943 Canadian academic awards ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Jeffery–Williams Prize
The Jeffery–Williams Prize is a mathematics award presented annually by the Canadian Mathematical Society. The award is presented to individuals in recognition of outstanding contributions to mathematical research. The first award was presented in 1968. The prize was named in honor of the mathematicians Ralph Lent Jeffery and Lloyd Williams. Recipients of the Jeffery–Williams Prize SourceCanadian Mathematical Society See also * List of mathematics awards This list of mathematics awards contains articles about notable awards for mathematics. The list is organized by the region and country of the organization that sponsors the award, but awards may be open to mathematicians from around the world. Som ... References External links Canadian Mathematical Society {{DEFAULTSORT:Jeffery-Williams Prize Awards of the Canadian Mathematical Society Awards established in 1968 1968 establishments in Canada ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Tutte's Fragment
In mathematics, Tait's conjecture states that "Every 3-connected planar cubic graph has a Hamiltonian cycle (along the edges) through all its vertices". It was proposed by and disproved by , who constructed a counterexample with 25 faces, 69 edges and 46 vertices. Several smaller counterexamples, with 21 faces, 57 edges and 38 vertices, were later proved minimal by . The condition that the graph be 3-regular is necessary due to polyhedra such as the rhombic dodecahedron, which forms a bipartite graph with six degree-four vertices on one side and eight degree-three vertices on the other side; because any Hamiltonian cycle would have to alternate between the two sides of the bipartition, but they have unequal numbers of vertices, the rhombic dodecahedron is not Hamiltonian. The conjecture was significant, because if true, it would have implied the four color theorem: as Tait described, the four-color problem is equivalent to the problem of finding 3-edge-colorings of bridgeles ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Cryptanalysis Of The Lorenz Cipher
Cryptanalysis of the Lorenz cipher was the process that enabled the British to read high-level German army messages during World War II. The British Government Code and Cypher School (GC&CS) at Bletchley Park decrypted many communications between the ''Oberkommando der Wehrmacht'' (OKW, German High Command) in Berlin and their army commands throughout occupied Europe, some of which were signed "Adolf Hitler, Führer". These were intercepted non-Morse code, Morse radio transmissions that had been enciphered by the Lorenz cipher, Lorenz SZ teleprinter Rotor machine, rotor stream cipher attachments. Decrypts of this traffic became an important source of "Ultra (cryptography), Ultra" intelligence, which contributed significantly to Allied victory. For its high-level secret messages, the German armed services enciphered each Character (computing), character using various online ''Geheimschreiber'' (secret writer) stream cipher machines at both ends of a Electrical telegraph, telegraph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Tutte–Grothendieck Invariant
In mathematics, a Tutte–Grothendieck (TG) invariant is a type of graph invariant that satisfies a generalized deletion–contraction formula. Any evaluation of the Tutte polynomial would be an example of a TG invariant. Definition A graph function ''f'' is TG-invariant if: f(G) = \begin c^ & \text \\ xf(G/e) & \text e \text \\ yf(G \backslash e) & \text e \text \\ af(G/e) + bf(G \backslash e) & \text \end Above ''G'' / ''e'' denotes edge contraction whereas ''G'' \ ''e'' denotes deletion. The numbers ''c'', ''x'', ''y'', ''a'', ''b'' are parameters. Generalization to matroids The matroid function ''f'' is TG if: : \begin &f(M_1\oplus M_2) = f(M_1)f(M_2) \\ &f(M) = a f(M \backslash e) + b f(M / e) \ \ \ \text e \text \end It can be shown that ''f'' is given by: : f(M) = a^b^ T(M; x_0/b, y_0/a) where is the value takes on coloops, is the value takes on loops, is the edge set of ; is the rank function; and : T(M; x, y) = \sum_ (x-1)^ (y-1)^ is the generalization ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |