The God has created a man in order that he creates that the God fails to do



Saturday 21 July 2012

What is a mathematical structure?


The notion of a mathematical structure was introduced at the beginning of XX century.
However, for a long time, mathematical objects were believed to be given always together with some structure, not necessarily unique, but at least natural (canonical). And only a practice, e.g., of functional analysis has led to conclusion that a canonical structure need not exist. For instance, there are different “natural” topologies of a set of rational numbers, different smooth structures of a 4-dimensional topological Euclidean space, different measures on a real line, and so on.

In mathematics, different types of structures are considered. These are an algebraic structure, a topological structure, cells whose notion generalizes the Boolean algebras and so on. In the first volume of their course, Bourbaki provide a description of a mathematical structure which enables them to define “espece de structure” and, thus, characterize and compare different structures. However, this is a structure of mathematical theories formulated in terms of logic. Therefore, one can suggest a wider definition of a structure which absorbs the Bourbaki one and the others, but can not characterize different types of structures.

This definition is based on the notion of a relation on a set and generalizes the definition of  a relational system in set theory.

Morphisms and functions are structures in this sense, and this fact provides a wide circle of applications of this notion of a structure to physics. 


Tuesday 10 July 2012

The Higgs boson or the Higgs vacuum?


In accordance with the Higgs mechanism of mass generation, quantum particles get a mass due to its interaction with a constant background classical field  responsible for spontaneous symmetry breaking. It is treated as a Higgs vacuum, but not a familiar quantum particle – a Higgs boson. The physical origin of such a Higgs vacuum is unclear. For instance, one thinks of it as being sue generis a condensate by analogy with a condensate of Cooper pairs in superconductivity.  What  then has been discovered?

Tuesday 3 July 2012

Impact Factor 2011 of Journals in Mathematical Physics


New Impact Factor 2011 has been announced.

Impact Factor 2011 of some journals closed to our International Journal of Geometric Methods in Modern Physics by subject and style is the following:

Journal Title

Impact Factor 2011
Impact Factor 2010
Impact Factor 2009
Impact Factor 2008
Impact Factor 2007
5-Year
Impact
Factor
1.941
2.000
2.067
2.075
2.070
1.998
1.819
0.842
0.969
0.916
1.044
1.223
1.564
1.641
1.577
1.540
1.680
1.344
1.291
1.291
1.318
1.085
1.137
1.181
1.213
1.290
1.190
1.258
1.386
1.032
IJGMMP (WS)
0.856
0.757
1.612
1.464
0.662
1.102
0.818
0.652
0.714
0.683
0.986
0.710
0.643
0.734
0.658
0.576
0.624
0.627


See Total List of journals in mathematical physics.

Of course, IF essentially depends on a research area. Of course, small journals of < 50 articles in a year have the advantage in IF.