Search results for "combinatoric"
showing 10 items of 1776 documents
p-Brauer characters ofq-defect 0
1994
For ap-solvable groupG the number of irreducible Brauer characters ofG with a given vertexP is equal to the number of irreducible Brauer characters of the normalizer ofP with vertexP. In this paper we prove in addition that for solvable groups one can control the number of those characters whose degrees are divisible by the largest possibleq-power dividing the order of |G|.
Variations on a Theorem of Fine & Wilf
2001
In 1965, Fine & Wilf proved the following theorem: if (fn)n≥0 and (gn)n≥0 are periodic sequences of real numbers, of periods h and k respectively, and fn = gn for 0 ≤ n ≤ h+k-gcd(h, k), then fn = gn for all n ≥ 0. Furthermore, the constant h + k - gcd(h, k) is best possible. In this paper we consider some variations on this theorem. In particular, we study the case where fn ≤ gn instead of fn = gn. We also obtain a generalization to more than two periods.
Polyomino Number Theory (II)
2003
Polyominoes are connected plane figures formed of joining unit squares edge to edge. We have a monomino, a domino, two trominoes named I and V, five tetrominoes named I, L, N, O and T, respectively, and twelve pentominoes (a registered trademark of Solomon W. Golomb) named F, I, L, N, P, T, U, V, W, X, Y and Z respectively.
Construction de Triplets Spectraux à Partir de Modules de Fredholm
1998
Soit (A, H, F) un module de Fredholm p-sommable, où l'algèbre A = CT est engendrée par un groupe discret Gamma d'éléments unitaires de L(H) qui est de croissance polynomiale r. On construit alors un triplet spectral (A, H, D) sommabilité q pour tout q > p + r + 1 avec F = signD. Dans le cas où (A, H, F) est (p, infini)-sommable on obtient la (q, infini)-sommabilité de (A, H, D)pour tout q > p + r + 1. Let (A, H, F) be a p-summable Fredholm module where the algebra A = CT is generated by a discrete group of unitaries in L(H) which is of polynomial growth r. Then we construct a spectral triple (A, H, D) with F = signD which is q-summable for each q > p + r + 1. In case (A, H, F) is (p, infini…
Optimization problem in inductive inference
1995
Algorithms recognizing to which of n classes some total function belongs are constructed (n > 2). In this construction strategies determining to which of two classes the function belongs are used as subroutines. Upper and lower bounds for number of necessary strategies are obtained in several models: FIN- and EX-identification and EX-identification with limited number of mindchanges. It is proved that in EX-identification it is necessary to use n(n−1)/2 strategies. In FIN-identification [3n/2 − 2] strategies are necessary and sufficient, in EX-identification with one mindchange- n log2n+o(n log2n) strategies.
Packing dimensions of sections of sets
1999
We obtain a formula for the essential supremum of the packing dimensions of the sections of sets parallel to a given subspace. This depends on a variant of packing dimension defined in terms of local projections of sets.
Packing a Trunk
2003
We report on a project with a German car manufacturer. The task is to compute (approximate) solutions to a specific large-scale packing problem. Given a polyhedral model of a car trunk, the aim is to pack as many identical boxes of size 4 × 2 × 1 units as possible into the interior of the trunk. This measure is important for car manufacturers, because it is a standard in the European Union.
Direct Evaluation of Path Integrals
2001
Every time τ n is assigned a point y n . We now connect the individual points with a classical path y(τ). y(τ) is not necessarily the (on-shell trajectory) extremum of the classical action. It can be any path between τ n and τn−1 specified by the classical Lagrangian \(L(y,\dot{y},t).\)
Order-disorder phase transition in random-walk networks
2004
In this paper we study in detail the behavior of random-walk networks (RWN's). These networks are a generalization of the well-known random Boolean networks (RBN's), a classical approach to the study of the genome. RWN's are also discrete networks, but their response is defined by small variations in the state of each gene, thus being a more realistic representation of the genome and a natural bridge between discrete and continuous models. RWN's show a clear transition between order and disorder. Here we explicitly deduce the formula of the critical line for the annealed model and compute numerically the transition points for quenched and annealed models. We show that RBN's and the annealed…
Berry’s Phase
2001
Let a physical system be described by a Hamiltonian with two sets of variables \(\boldsymbol{r}\) and \(\boldsymbol{R}(t):\, H(\boldsymbol{r},\boldsymbol{R}(t)).\) The dynamical degrees of freedom \(\boldsymbol{r}\) (not necessarily space variables) are also called fast variables. The external time dependence is given by the slowly varying parameters \(\boldsymbol{R}(t) =\{ X(t),\,Y (t),\,\ldots,\,Z(t)\}\); consequently, the \(\boldsymbol{R}(t)\) are called slow variables.