scholarly journals Commentary: The burden of conceptual proof

2020 ◽  
Author(s):  
J.W. Awori Hayanga
Keyword(s):  
Conceptual Proof

A Conceptual Proof of Cramer's Rule

2004 ◽  
Vol 77 (4) ◽  
pp. 308
Author(s):  
Richard Ehrenborg
Keyword(s):  
Conceptual Proof ◽  
Cramer’S Rule

scholarly journals Supercritical multitype branching processes: the ancestral types of typical individuals

2003 ◽  
Vol 35 (4) ◽  
pp. 1090-1110 ◽  
Author(s):  
Hans-Otto Georgii ◽  
Ellen Baake
Keyword(s):  
Continuous Time ◽  
Branching Processes ◽  
Almost Sure Convergence ◽  
Family Tree ◽  
Mutation Process ◽  
Convergence Theorems ◽  
Conceptual Proof ◽  
The Family ◽  
Multitype Branching Processes

For supercritical multitype Markov branching processes in continuous time, we investigate the evolution of types along those lineages that survive up to some time t. We establish almost-sure convergence theorems for both time and population averages of ancestral types (conditioned on nonextinction), and identify the mutation process describing the type evolution along typical lineages. An important tool is a representation of the family tree in terms of a suitable size-biased tree with trunk. As a by-product, this representation allows a ‘conceptual proof’ (in the sense of Kurtz et al.) of the continuous-time version of the Kesten-Stigum theorem.

scholarly journals QUANTUM GROUPS, q-BOSON ALGEBRAS AND QUANTIZED WEYL ALGEBRAS

2011 ◽  
Vol 22 (05) ◽  
pp. 675-694 ◽  
Author(s):  
XIN FANG
Keyword(s):  
Quantum Groups ◽  
Weyl Algebras ◽  
Conceptual Proof

We give a unified construction of quantum groups, q-boson algebras and quantized Weyl algebras and an action of quantum groups on quantized Weyl algebras. This enables us to give a conceptual proof of the semi-simplicity of the category [Formula: see text] introduced by Nakashima and the classification of all simple objects in it.

scholarly journals Prime Decomposition of Three-Dimensional Manifolds into Boundary Connected Sum

2014 ◽  
Vol 2014 ◽  
pp. 1-3
Author(s):  
Meili Zhang ◽  
Bo Deng
Keyword(s):  
Three Dimensional ◽  
Prime Decomposition ◽  
Connected Sum ◽  
Conceptual Proof

In 2003 Matveev suggested a new version of the Diamond Lemma suitable for topological applications. We apply this result to different situations and get a new conceptual proof of theorem on decomposition of three-dimensional manifolds into boundary connected sum of prime components.

scholarly journals Supercritical multitype branching processes: the ancestral types of typical individuals

2003 ◽  
Vol 35 (04) ◽  
pp. 1090-1110 ◽  
Author(s):  
Hans-Otto Georgii ◽  
Ellen Baake
Keyword(s):  
Continuous Time ◽  
Branching Processes ◽  
Almost Sure Convergence ◽  
Family Tree ◽  
Mutation Process ◽  
Convergence Theorems ◽  
Conceptual Proof ◽  
The Family ◽  
Multitype Branching Processes

For supercritical multitype Markov branching processes in continuous time, we investigate the evolution of types along those lineages that survive up to some time t. We establish almost-sure convergence theorems for both time and population averages of ancestral types (conditioned on nonextinction), and identify the mutation process describing the type evolution along typical lineages. An important tool is a representation of the family tree in terms of a suitable size-biased tree with trunk. As a by-product, this representation allows a ‘conceptual proof’ (in the sense of Kurtz et al.) of the continuous-time version of the Kesten-Stigum theorem.

A REAPPEARANCE OF WHEELS

1998 ◽  
Vol 07 (08) ◽  
pp. 1065-1071
Author(s):  
STAVROS GAROUFALIDIS
Keyword(s):  
Power Series ◽  
Finite Type ◽  
Present Note ◽  
Chinese Characters ◽  
Rational Homology ◽  
Universal Formula ◽  
Type Invariant ◽  
Conceptual Proof ◽  
Number Of Authors

Recently, a number of authors [KS, Oh2, Ro] have independently shown that the universal finite type invariant of rational homology 3-spheres on the level of [Formula: see text] can be recovered from the Reshetikhin-Turaev [Formula: see text] invariant. An important role in Ohtsuki's proof [Oh3] plays a map j1 (which joins the legs of 2-legged chinese characters) and its relation to a map α in terms of a power series (on the level of [Formula: see text]). The purpose of the present note is to give a universal formula of the map α in terms of a power series F of wheel chinese characters. The above formula is similar to universal formulas of wheel chinese characters considered in [BGRT1] and leads to a simple conceptual proof of the above mentioned relation between the maps j1 and α on the level of [Formula: see text].

scholarly journals Drinfeld Realization of Quantum Twisted Affine Algebras via Braid Group

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Naihuan Jing ◽  
Honglian Zhang
Keyword(s):  
Group Action ◽  
Braid Group ◽  
Previous Approach ◽  
Quantum Affine Algebras ◽  
Conceptual Proof ◽  
Affine Algebras ◽  
Braid Group Action

The Drinfeld realization of quantum affine algebras has been tremendously useful since its discovery. Combining techniques of Beck and Nakajima with our previous approach, we give a complete and conceptual proof of the Drinfeld realization for the twisted quantum affine algebras using Lusztig’s braid group action.

Polar representations and symmetric spaces

1999 ◽  
Vol 1999 (507) ◽  
pp. 93-106 ◽  
Author(s):  
J.-H Eschenburg ◽  
E Heintze
Keyword(s):  
Symmetric Space ◽  
Symmetric Spaces ◽  
Isotropy Representation ◽  
Polar Representation ◽  
Conceptual Proof

Abstract J. Dadok has shown by classification that any polar representation has the same orbits as the isotropy representation of some symmetric space. A conceptual proof of this result is given subject to some restriction.

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