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...Laureate is based upon the recommendation by the Abel Committee consisting of five internationally recognized mathematicians, and is handed over by the King of Norway in an official ceremony. Both Jean-Pierre Serre and Mikhail L. Gromo ...

===Quantum automaton and quantum computation=== ...m states instead of the sequentially determined states, inputs and outputs of a ''sequential, or state machine'' . ...

{{nav3|Wikiversity|Wikiversity:School of Computer Science|Wikiversity:Theory}} ...ed with the purely syntactical aspects, rather than a semantics or meaning of the strings<ref name="wikipedia">Wikipedia, https://en.wikipedia.org/wiki/F ...

There are several generalizations of the original extension to crossed complexes, its extension in categorical form in terms of colimits, and its generalization to higher dimensions, i.e., its extension ...

...s. A central problem in algebraic topology is to find algebraic invariants of topological spaces, which is usually carried out by means ...ogy, Algebraic Geometry (AG), [[../NAQAT2/|non-commutative geometry]] and, of course, its most recent development-- ...

This is a commentary of the preprint<ref name="ddr20"/> by Das, Datta and Raman. .... Computing the blocks efficiently is important for numerical calculations of correlation functions. ...

...e in terms of so-called `j-symbols' as further detailed next. The vertices of the tetrahedron are located at the points <math>(a_x, a_y, a_z)</math>, <ma vertices of the tetrahedron, and thus also assigns a `direction' to each edge of the tetrahedron--from the ...

...ints/An Explanation for Expansion of the Universe from Whittaker Potential Theory}} ...ints/An Explanation for Expansion of the Universe from Whittaker Potential Theory}} ...

...ose for other known critical exponents. In particular, in the special case of critical percolation, the backbone exponent is a transcendent number, while The determination of the backbone exponent raises two questions: ...

...etphysics.org/?op=getobj&from=lec&id=119 EPR `Paradox']; several solutions of the a. Interpretations of experiments with polarized laser beams ...

...mplex <math>K</math> : the Betti number-which is the number of repetitions of <math>Z</math> in the homology group, ...number <math>p</math> gives the number of <math>p</math>-dimensional turns of <math>K</math>. ...

...e of spacetime. In fact, "general relativity" and "Einstein's formulation of gravity" are nearly synonymous in many people's minds. The general theory of relativity was first published by [[Albert Einstein]] in 1916. ...

...tions were suggested to be insufficient, and alternative theories in terms of topological ...ethodsForQuantizedSpacetimes2/|Quantum Algebraic Topology]] means in terms of [[../Groupoid/|quantum operator algebras]] and [[../UcLocallyCompactQuantum ...

...opy groupoids. He then completed the studies on pure higher order category theory in a publication with F.A. Al-Agl and R. Steiner, on "Multiple categories: ...[../SingularComplexOfASpace/|generalized Van Kampen theorems]] in homotopy theory[3]. ...

...AdjointnessAndTopologicalEquivalence/|systems]] (e.g. the axiomatic theory of [[../SuperCategory6/|supercategories]]); these are currently being studied ...algebra and geometry, which early appeared in category theory with the use of complex [[../Commutativity/|commutative diagrams]]. What is needed next is ...

...poid/|algebraic topology]]. In physics they are important to the treatment of [[../Vectors/|vectors]] and other quantities, such as [[../Tensor/|tensors] ...the same footing. This is of basic importance in the practical application of tensors. ...

...complete these computations (analytically), and to check crossing symmetry of four-point functions (numerically and/or analytically). ...y. It is the basis for the worldsheet approach to [[w:String theory|string theory]] in <math>AdS_3</math>, and it is closely related to the Witten black hole ...

...ophical principle ideas in biology and sociology in terms of the emergence of higher [[../Complexity/|complexity]] levels in living [[../SimilarityAndAna ...bras]] ([[../2Groupoid2/|HDA]]). Therefore, [[../TrivialGroupoid/|category theory]] in higher dimensions/HDA ...

...s <math>\{ \operatorname{false}, \operatorname{true} \}.</math> The names of the logical values, or ''truth values'', are commonly abbreviated in accord ...all representation of truth functions as boolean functions. The remainder of this article assumes the usual representation, taking the equations <math>\ ...

...inguished from, though closely related to, its study from the perspectives of abstract algebra on the one hand and formal logic on the other. Two definitions of the relation concept are common in the literature. Although it is usually ...