Search results for "combinatoric"
showing 10 items of 1776 documents
Primitive characters of subgroups ofM-groups
1995
One of the hardest areas in the Character Theory of Solvable Groups continues to be the monomial groups. A finite group is said to be an M-group (or monomial) if all of its irreducible characters are monomial, that is to say, induced from linear characters. Two are still the main problems on M-groups: are Hall subgroups of M groups monomial? Under certain oddness hypothesis, are normal subgroups of M-groups monomial? In both cases there is evidence that this could be the case: the primitive characters of the subgroups in question are the linear characters. This is the best result up to date ([4], [6]). Recently, some idea appears to be taking form. In [14], T. Okuyama proved that if G is an…
Affine Surfaces With a Huge Group of Automorphisms
2013
We describe a family of rational affine surfaces S with huge groups of automorphisms in the following sense: the normal subgroup Aut(S)alg of Aut(S) generated by all algebraic subgroups of Aut(S) is not generated by any countable family of such subgroups, and the quotient Aut(S)/Aut(S)alg cointains a free group over an uncountable set of generators.
Quantum algorithms for search with wildcards and combinatorial group testing
2012
We consider two combinatorial problems. The first we call "search with wildcards": given an unknown n-bit string x, and the ability to check whether any subset of the bits of x is equal to a provided query string, the goal is to output x. We give a nearly optimal O(sqrt(n) log n) quantum query algorithm for search with wildcards, beating the classical lower bound of Omega(n) queries. Rather than using amplitude amplification or a quantum walk, our algorithm is ultimately based on the solution to a state discrimination problem. The second problem we consider is combinatorial group testing, which is the task of identifying a subset of at most k special items out of a set of n items, given the…
Limits on entropic uncertainty relations
2010
We consider entropic uncertainty relations for outcomes of the measurements of a quantum state in 3 or more mutually unbiased bases (MUBs), chosen from the standard construction of MUBs in prime dimension. We show that, for any choice of 3 MUBs and at least one choice of a larger number of MUBs, the best possible entropic uncertainty relation can be only marginally better than the one that trivially follows from the relation by Maassen and Uffink for 2 bases.
Measurement ofD0−D¯0mixing using the ratio of lifetimes for the decaysD0→K−π+andK+K−
2009
We present a measurement of ${D}^{0}\mathrm{\text{\ensuremath{-}}}{\overline{D}}^{0}$ mixing and $CP$ violation using the ratio of lifetimes simultaneously extracted from a sample of ${D}^{0}$ mesons produced through the flavor-tagged process ${D}^{*+}\ensuremath{\rightarrow}{D}^{0}{\ensuremath{\pi}}^{+}$, where ${D}^{0}$ decays to ${K}^{\ensuremath{\mp}}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$, ${K}^{\ensuremath{-}}{K}^{+}$, or ${\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$, along with the untagged decays ${D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{\mp}}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ and ${D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{K}…
Correcting for Potential Barriers in Quantum Walk Search
2015
A randomly walking quantum particle searches in Grover's $\Theta(\sqrt{N})$ iterations for a marked vertex on the complete graph of $N$ vertices by repeatedly querying an oracle that flips the amplitude at the marked vertex, scattering by a "coin" flip, and hopping. Physically, however, potential energy barriers can hinder the hop and cause the search to fail, even when the amplitude of not hopping decreases with $N$. We correct for these errors by interpreting the quantum walk search as an amplitude amplification algorithm and modifying the phases applied by the coin flip and oracle such that the amplification recovers the $\Theta(\sqrt{N})$ runtime.
Two-step nilpotent Leibniz algebras
2022
In this paper we give a complete classification of two-step nilpotent Leibniz algebras in terms of Kronecker modules associated with pairs of bilinear forms. In particular, we describe the complex and the real case of the indecomposable Heisenberg Leibniz algebras as a generalization of the classical $(2n+1)-$dimensional Heisenberg Lie algebra $\mathfrak{h}_{2n+1}$. Then we use the Leibniz algebras - Lie local racks correspondence proposed by S. Covez to show that nilpotent real Leibniz algebras have always a global integration. As an application, we integrate the indecomposable nilpotent real Leibniz algebras with one-dimensional commutator ideal. We also show that every Lie quandle integr…
On the condition number of the antireflective transform
2010
Abstract Deconvolution problems with a finite observation window require appropriate models of the unknown signal in order to guarantee uniqueness of the solution. For this purpose it has recently been suggested to impose some kind of antireflectivity of the signal. With this constraint, the deconvolution problem can be solved with an appropriate modification of the fast sine transform, provided that the convolution kernel is symmetric. The corresponding transformation is called the antireflective transform. In this work we determine the condition number of the antireflective transform to first order, and use this to show that the so-called reblurring variant of Tikhonov regularization for …
Explicit solutions for second-order operator differential equations with two boundary-value conditions. II
1992
AbstractBoundary-value problems for second-order operator differential equations with two boundary-value conditions are studied for the case where the companion operator is similar to a block-diagonal operator. This case is strictly more general than the one treated in an earlier paper, and it provides explicit closed-form solutions of boundary-value problem in terms of data without increasing the dimension of the problem.
Separation properties of (n, m)-IFS attractors
2017
Abstract The separation properties of self similar sets are discussed in this article. An open set condition for the (n, m)- iterated function system is introduced and the concepts of self similarity, similarity dimension and Hausdorff dimension of the attractor generated by an (n, m) - iterated function system are studied. It is proved that the similarity dimension and the Hausdorff dimension of the attractor of an (n, m) - iterated function system are equal under this open set condition. Further a necessary and sufficient condition for a set to satisfy the open set condition is established.