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Arne Beurling
Arne Carl-August Beurling (3 February 1905 – 20 November 1986) was a Swedish mathematician and professor of mathematics at Uppsala University (1937–1954) and later at the Institute for Advanced Study in Princeton, New Jersey. Beurling worked extensively in harmonic analysis, complex analysis and potential theory. The " Beurling factorization" helped mathematical scientists to understand the Wold decomposition, and inspired further work on the invariant subspaces of linear operators and operator algebras, e.g. Håkan Hedenmalm's factorization theorem for Bergman spaces. He is perhaps most famous for single-handedly decrypting an early version of the German cipher machine Siemens and Halske T52 in a matter of two weeks during 1940, using only pen and paper. This machine's cipher is generally considered to be more complicated than that of the more famous Enigma machine. Early life Beurling was born on 3 February 1905 in Gothenburg, Sweden and was the son of the landowner Kon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gothenburg
Gothenburg (; abbreviated Gbg; sv, Göteborg ) is the second-largest city in Sweden, fifth-largest in the Nordic countries, and capital of the Västra Götaland County. It is situated by the Kattegat, on the west coast of Sweden, and has a population of approximately 590,000 in the city proper and about 1.1 million inhabitants in the metropolitan area. Gothenburg was founded as a heavily fortified, primarily Dutch, trading colony, by royal charter in 1621 by King Gustavus Adolphus. In addition to the generous privileges (e.g. tax relaxation) given to his Dutch allies from the ongoing Thirty Years' War, the king also attracted significant numbers of his German and Scottish allies to populate his only town on the western coast. At a key strategic location at the mouth of the Göta älv, where Scandinavia's largest drainage basin enters the sea, the Port of Gothenburg is now the largest port in the Nordic countries. Gothenburg is home to many students, as the city includes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reverse Engineering
Reverse engineering (also known as backwards engineering or back engineering) is a process or method through which one attempts to understand through deductive reasoning how a previously made device, process, system, or piece of software accomplishes a task with very little (if any) insight into exactly how it does so. It is essentially the process of opening up or dissecting a system to see how it works, in order to duplicate or enhance it. Depending on the system under consideration and the technologies employed, the knowledge gained during reverse engineering can help with repurposing obsolete objects, doing security analysis, or learning how something works. Although the process is specific to the object on which it is being performed, all reverse engineering processes consist of three basic steps: Information extraction, Modeling, and Review. Information extraction refers to the practice of gathering all relevant information for performing the operation. Modeling refers to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decipher
DECIPHER is a web-based resource and database of genomic variation data from analysis of patient DNA. It documents submicroscopic Chromosome abnormality, chromosome abnormalities (Deletion (genetics), microdeletions and Gene duplication, duplications) and pathogenic sequence variants (single nucleotide variants - SNVs, Insertions, Deletions, InDels), from over 25000 patients and maps them to the human genome using Ensembl or UCSC Genome Browser. In addition it catalogues the clinical characteristics from each patient and maintains a database of microdeletion/duplication syndromes, together with links to relevant scientific reports and support groups. An acronym of DatabasE of Chromosomal Imbalance and Phenotype in Humans using Ensembl Resources, DECIPHER was initiated in 2004 at the Wellcome Trust Sanger Institute, Sanger Institute in the United Kingdom, funded by the Wellcome Trust. However it is supported by an international research consortium, with patient data contributed b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Docent
The title of docent is conferred by some European universities to denote a specific academic appointment within a set structure of academic ranks at or below the full professor rank, similar to a British readership, a French " ''maître de conférences''" (MCF), and equal to or above the title of " associate professor". Docent is also used at some (mainly German) universities generically for a person who has the right to teach. The term is derived from the Latin word ''docēns'', which is the present active participle of ''docēre'' (to teach, to lecture). Becoming a docent is often referred to as Habilitation or doctor of science and is an academic qualification that shows that the holder is qualified to be employed at the level of associate or full professor. Docent is the highest academic title in several countries, and the qualifying criteria are research output that corresponds to 3-5 doctoral dissertations, supervision of PhD students, and experience in teaching at the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Studentexamen
Studentexamen (Swedish for "students' examination" or "students' degree"), earlier also ''mogenhetsexamen'' ("maturity examination") was the name of the university entrance examination in Sweden from the 17th century to 1968. From 1862 to 1968, it was taken as a final written and oral exam on graduation from gymnasium (secondary school). In Finland the examination (Finnish: ''Ylioppilastutkinto'') still exists (Finland parted from Sweden 1809). The exam traces its origin to the academic statutes from 1655 requiring the dean to examine students arriving at university before allowing matriculation. According to the school reglement of 1693, a prospective student was to have gone through both a final examination at school and an entrance examination at university. The school reglement of 1724 allowed students without a final examination from school to enroll at university, provided a person known at the university would guarantee their behaviour, which led to it becoming common f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Siemens And Halske T52
The Siemens & Halske T52, also known as the Geheimschreiber ("secret teleprinter"), or ''Schlüsselfernschreibmaschine'' (SFM), was a World War II German cipher machine and teleprinter produced by the electrical engineering firm Siemens & Halske. The instrument and its traffic were codenamed ''Sturgeon'' by British cryptanalysts. While the Enigma machine was generally used by field units, the T52 was an online machine used by Luftwaffe and German Navy units, which could support the heavy machine, teletypewriter and attendant fixed circuits. It fulfilled a similar role to the Lorenz cipher machines in the German Army. The British cryptanalysts of Bletchley Park codenamed the German teleprinter ciphers Fish, with individual cipher-systems being given further codenames: just as the T52 was called ''Sturgeon'', the Lorenz machine was codenamed ''Tunny''. Operation The teleprinters of the day emitted each character as five parallel bits on five lines, typically encoded in the Baudo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bergman Space
In complex analysis, functional analysis and operator theory, a Bergman space, named after Stefan Bergman, is a function space of holomorphic functions in a domain ''D'' of the complex plane that are sufficiently well-behaved at the boundary that they are absolutely integrable. Specifically, for , the Bergman space is the space of all holomorphic functions f in ''D'' for which the p-norm is finite: :\, f\, _ := \left(\int_D , f(x+iy), ^p\,\mathrm dx\,\mathrm dy\right)^ < \infty. The quantity is called the ''norm'' of the function ; it is a true if . Thus is the subspace of holomorphic functions that are in the space L''p''(''D''). The Bergman spaces are |
Operator Algebras
In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication given by the composition of mappings. The results obtained in the study of operator algebras are phrased in algebraic terms, while the techniques used are highly analytic.''Theory of Operator Algebras I'' By Masamichi Takesaki, Springer 2012, p vi Although the study of operator algebras is usually classified as a branch of functional analysis, it has direct applications to representation theory, differential geometry, quantum statistical mechanics, quantum information, and quantum field theory. Overview Operator algebras can be used to study arbitrary sets of operators with little algebraic relation ''simultaneously''. From this point of view, operator algebras can be regarded as a generalization of spectral theory of a single operator. In general operator algebras are non-commutative rings. An operator alge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Invariant Subspace
In mathematics, an invariant subspace of a linear mapping ''T'' : ''V'' → ''V '' i.e. from some vector space ''V'' to itself, is a subspace ''W'' of ''V'' that is preserved by ''T''; that is, ''T''(''W'') ⊆ ''W''. General description Consider a linear mapping T :T: W \to W. An invariant subspace W of T has the property that all vectors \mathbf \in W are transformed by T into vectors also contained in W. This can be stated as :\mathbf \in W \implies T(\mathbf) \in W. Trivial examples of invariant subspaces * \mathbb^n: Since T maps every vector in \mathbb^n into \mathbb^n. * \: Since a linear map has to map 0 \mapsto 0. 1-dimensional invariant subspace ''U'' A basis of a 1-dimensional space is simply a non-zero vector \mathbf. Consequently, any vector \mathbf \in U can be represented as \lambda \mathbf where \lambda is a scalar. If we represent T by a matrix A then, for U to be an invariant subspace it must satisfy : \forall \mathbf \in U \; \exists \alpha \in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wold Decomposition
In mathematics, particularly in operator theory, Wold decomposition or Wold–von Neumann decomposition, named after Herman Wold and John von Neumann, is a classification theorem for isometric linear operators on a given Hilbert space. It states that every isometry is a direct sum of copies of the unilateral shift and a unitary operator. In time series analysis, the theorem implies that any stationary discrete-time stochastic process can be decomposed into a pair of uncorrelated processes, one deterministic, and the other being a moving average process. Details Let ''H'' be a Hilbert space, ''L''(''H'') be the bounded operators on ''H'', and ''V'' ∈ ''L''(''H'') be an isometry. The Wold decomposition states that every isometry ''V'' takes the form :V = (\oplus_ S) \oplus U for some index set ''A'', where ''S'' is the unilateral shift on a Hilbert space ''Hα'', and ''U'' is a unitary operator (possible vacuous). The family consists of isomorphic Hilbert spaces. A proof ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
