4,434 research outputs found
Invariable generation and the chebotarev invariant of a finite group
A subset S of a finite group G invariably generates G if G = <hsg(s) j s 2 Si
> for each choice of g(s) 2 G; s 2 S. We give a tight upper bound on the
minimal size of an invariable generating set for an arbitrary finite group G.
In response to a question in [KZ] we also bound the size of a randomly chosen
set of elements of G that is likely to generate G invariably. Along the way we
prove that every finite simple group is invariably generated by two elements.Comment: Improved versio
A Model Ground State of Polyampholytes
The ground state of randomly charged polyampholytes is conjectured to have a
structure similar to a necklace, made of weakly charged parts of the chain,
compacting into globules, connected by highly charged stretched `strings'. We
suggest a specific structure, within the necklace model, where all the neutral
parts of the chain compact into globules: The longest neutral segment compacts
into a globule; in the remaining part of the chain, the longest neutral segment
(the 2nd longest neutral segment) compacts into a globule, then the 3rd, and so
on. We investigate the size distributions of the longest neutral segments in
random charge sequences, using analytical and Monte Carlo methods. We show that
the length of the n-th longest neutral segment in a sequence of N monomers is
proportional to N/(n^2), while the mean number of neutral segments increases as
sqrt(N). The polyampholyte in the ground state within our model is found to
have an average linear size proportional to sqrt(N), and an average surface
area proportional to N^(2/3).Comment: 8 two-column pages. 5 eps figures. RevTex. Submitted to Phys. Rev.
Synergetic modelling of the Russian Federation’s energy system parameters
The energy system in any country is the basis of the whole economy. The level of its development largely determines the quantity and quality of economic entities, periods of economic growth, fall and stagnation. A high percentage of the power-deficient municipalities in the Russian Federation shows the substantive issues in this sphere that carries a threat to the energy security of the state. One of the promising trends for enhancing the energy security is the renewable energy sources (RES). Their use has the obvious benefits: it provides electricity to power-deficient and inaccessible areas, contributes to the introduction and spread of new technologies, thus solving the important social and economic problem. At that, it is important to determine the optimum ratio using of the recovery of renewable and conventional energy sources (CES). One of the main challenges in this regard is to build a model that adequately reflects the ratio of renewable and conventional energy sources in the Russian energy system. The paper presents the results of a synergistic approach to the construction of such a model. The Lotka- Volterra model was the main instrument used, which allowed to study a behavior pattern of the considered systems on the basis of the simplified regularities. It was found that the best possible qualitative “jump” in the Russian energy sector was in 2008. The calculations allowed to investigate the behavior of the Russian energy system with the variation of the initial conditions and to assess the validity of the targets for the share of electricity produced through the use of renewable energy in the total electric power of the country
MUBs inequivalence and affine planes
There are fairly large families of unitarily inequivalent complete sets of
N+1 mutually unbiased bases (MUBs) in C^N for various prime powers N. The
number of such sets is not bounded above by any polynomial as a function of N.
While it is standard that there is a superficial similarity between complete
sets of MUBs and finite affine planes, there is an intimate relationship
between these large families and affine planes. This note briefly summarizes
"old" results that do not appear to be well-known concerning known families of
complete sets of MUBs and their associated planes.Comment: This is the version of this paper appearing in J. Mathematical
Physics 53, 032204 (2012) except for format changes due to the journal's
style policie
Berezinians, Exterior Powers and Recurrent Sequences
We study power expansions of the characteristic function of a linear operator
in a -dimensional superspace . We show that traces of exterior
powers of satisfy universal recurrence relations of period .
`Underlying' recurrence relations hold in the Grothendieck ring of
representations of \GL(V). They are expressed by vanishing of certain Hankel
determinants of order in this ring, which generalizes the vanishing of
sufficiently high exterior powers of an ordinary vector space. In particular,
this allows to explicitly express the Berezinian of an operator as a rational
function of traces. We analyze the Cayley--Hamilton identity in a superspace.
Using the geometric meaning of the Berezinian we also give a simple formulation
of the analog of Cramer's rule.Comment: 35 pages. LaTeX 2e. New version: paper substantially reworked and
expanded, new results include
The Diuretic action of carbonic anhydrase inhibitor (Diamos) on cirrhosis of the liver : a case study of three patients with cirrhosis of the liver and associated ascites
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